R.D. Sharma solutions for Mathematics [English] Class 8 chapter 7 - Factorization [Latest edition]

Find the greatest common factor (GCF/HCF) of the following polynomial:
2x² and 12x²

Find the greatest common factor (GCF/HCF) of the following polynomial:
7x, 21x² and 14xy²

Find the greatest common factor (GCF/HCF) of the following polynomial:
12ax², 6a²x³ and 2a³x⁵

Find the greatest common factor (GCF/HCF) of the following polynomial:
9x², 15x²y³, 6xy² and 21x²y²

Find the greatest common factor (GCF/HCF) of the following polynomial:
4a²b³, −12a³b, 18a⁴b³

Find the greatest common factor (GCF/HCF) of the following polynomial:
6x²y², 9xy³, 3x³y²

Find the greatest common factor (GCF/HCF) of the following polynomial:
a²b³, a³b²

Find the greatest common factor (GCF/HCF) of the following polynomial:
36a²b²c⁴, 54a⁵c², 90a⁴b²c²

Find the greatest common factor (GCF/HCF) of the following polynomial:
x³, − yx²

Find the greatest common factor (GCF/HCF) of the following polynomial:
15a³, − 45a², − 150a

Find the greatest common factor (GCF/HCF) of the following polynomial:
2x³y², 10x²y³, 14xy

Find the greatest common factor (GCF/HCF) of the following polynomial:
14x³y⁵, 10x⁵y³, 2x²y²

Find the greatest common factor of the terms in each of the following expression:
5a⁴ + 10a³ − 15a²

Find the greatest common factor of the terms in each of the following expression:
2xyz + 3x²y + 4y²

Find the greatest common factor of the terms in each of the following expression:
3a²b² + 4b²c² + 12a²b²c²

Factorize the following:
3x − 9

Factorize the following:
5x − 15x²

Factorize the following:
20a¹²b² − 15a⁸b⁴

Factorize the following:
72x⁶y⁷ − 96x⁷y⁶

Factorize the following:
20x³ − 40x² + 80x

Factorize the following:
2x³y² − 4x²y³ + 8xy⁴

Factorize the following:
10m³n² + 15m⁴n − 20m²n³

Factorize the following:
2a⁴b⁴ − 3a³b⁵ + 4a²b⁵

Factorize the following:
28a² + 14a²b² − 21a⁴

Factorize the following:
a⁴b − 3a²b² − 6ab³

Factorize the following:
2l²mn - 3lm²n + 4lmn²

Factorize the following:
x⁴y² − x²y⁴ − x⁴y⁴

Factorize the following:
9x²y + 3axy

Factorize the following:
16m − 4m²

Factorize the following:
x²yz + xy²z + xyz²

Factorize the following:
ax²y + bxy² + cxyz

Factorize each of the following algebraic expressions:
6x(2x − y) + 7y(2x − y)

Factorize each of the following algebraic expressions:
2r(y − x) + s(x − y)

Factorize each of the following algebraic expressions:
7a(2x − 3) + 3b(2x − 3)

Factorize each of the following algebraic expressions:
9a(6a − 5b) −12a²(6a − 5b)

Factorize each of the following algebraic expressions:
5(x − 2y)² + 3(x − 2y)

Factorize each of the following algebraic expressions:
16(2l − 3m)² −12(3m − 2l)

Factorize each of the following algebraic expressions:
3a(x − 2y) −b(x − 2y)

Factorize each of the following algebraic expressions:
a²(x + y) +b²(x + y) +c²(x + y)

Factorize each of the following algebraic expressions:
(x − y)² + (x − y)

Factorize each of the following algebraic expressions:
6(a + 2b) −4(a + 2b)²

Factorize each of the following algebraic expressions:
a(x − y) + 2b(y − x) + c(x − y)²

Factorize each of the following algebraic expressions:
−4(x − 2y)² + 8(x −2y)

Factorize each of the following algebraic expressions:
x³(a − 2b) + x²(a − 2b)

Factorize each of the following algebraic expressions:
(2x − 3y)(a + b) + (3x − 2y)(a + b)

Factorize each of the following algebraic expressions:
4(x + y) (3a − b) +6(x + y) (2b − 3a)

Factorize each of the following expressions:
qr − pr + qs − ps

Factorize each of the following expressions:
p²q − pr² − pq + r²

Factorize each of the following expressions:
1 + x + xy + x²y

Factorize each of the following expressions:
ax + ay − bx − by

Factorize each of the following expressions:
xa² + xb² − ya² − yb²

Factorize each of the following expressions:
x² + xy + xz + yz

Factorize each of the following expressions:
2ax + bx + 2ay + by

Factorize each of the following expressions:
ab − by − ay + y²

Factorize each of the following expressions:
axy + bcxy − az − bcz

Factorize each of the following expressions:
lm² − mn² − lm + n²

Factorize each of the following expressions:
x³ − y² + x − x²y²

Factorize each of the following expressions:
6xy + 6 − 9y − 4x

Factorize each of the following expressions:
x² − 2ax − 2ab + bx

Factorize each of the following expressions:
x³ − 2x²y + 3xy² − 6y³

Factorize each of the following expression:
abx² + (ay − b) x − y

Factorize each of the following expression:
(ax + by)² + (bx − ay)²

Factorize each of the following expression:
16(a − b)³ − 24 (a − b)²

Factorize each of the following expression:
ab(x² + 1) + x(a² + b²)

Factorize each of the following expression:
a²x² + (ax² + 1)x + a

Factorize each of the following expression:
a(a − 2b − c) + 2bc

Factorize each of the following expression:
a(a + b − c) − bc

Factorize each of the following expression:
x² − 11xy − x + 11y

Factorize each of the following expression:
ab − a − b + 1

Factorize each of the following expression:
x² + y − xy − x

Factorize each of the following expression:
16x² − 25y²

Factorize each of the following expression:
27x² − 12y²

Factorize each of the following expression:
144a² − 289b²

Factorize each of the following expression:
12m² − 27

Factorize each of the following expression:
125x² − 45y²

Factorize each of the following expression:
144a² − 169b²

Factorize each of the following expression:
(2a − b)² − 16c²

Factorize each of the following expression:
(x + 2y)² − 4(2x − y)²

Factorize each of the following expression:
3a⁵ − 48a³

Factorize each of the following expression:
a⁴ − 16b⁴

Factorize each of the following expression:
64 − (a + 1)²

Factorize each of the following expression:
36l² − (m + n)²

Factorize each of the following expression:
25x⁴y⁴ − 1

Factorize each of the following expression:

Factorize each of the following expression:
x³ − 144x

Factorize each of the following expression:
(x - 4y)² − 625

Factorize each of the following expression:
9(a − b)² − 100(x − y)²

Factorize each of the following expression:
(3 + 2a)² − 25a²

Factorize each of the following expression:
(x + y)² − (a − b)²

Factorize each of the following expression:
\[\frac{1}{16} x^2 y^2 - \frac{4}{49} y^2 z^2\]

Factorize each of the following expression:
75a³b² - 108ab⁴

Factorize each of the following expression:
x⁵ − 16x³

Factorize each of the following expression:

Factorize each of the following expression:
256x⁵ − 81x

Factorize each of the following expression:
a⁴ − (2b + c)⁴

Factorize each of the following expression:
(3x + 4y)⁴ − x⁴

Factorize each of the following expression:
p²q² − p⁴q⁴

Factorize each of the following expression:
3x³y − 243xy³

Factorize each of the following expression:
a⁴b⁴ − 16c⁴

Factorize each of the following expression:
x⁴ − 625

Factorize each of the following expression:
49(a − b)² − 25(a + b)²

Factorize each of the following expression:
x − y − x² + y²

Factorize each of the following expression:
16(2x − 1)² − 25y²

Factorize each of the following expression:
(2x + 1)² − 9x⁴

Factorize each of the following expression:
x⁴ − (2y − 3z)²

Factorize each of the following expression:
a² − b² + a − b

Factorize each of the following expression:
16a⁴ − b⁴

Factorize each of the following expression:
a⁴ − 16(b − c)⁴

Factorize each of the following expression:
2a⁵ − 32a

Factorize each of the following expression:
a⁴b⁴ − 81c⁴

Factorize each of the following expression:
xy⁹ − yx⁹

Factorize each of the following expression:
x³ − x

Factorize each of the following expression:
18a²x² − 32

Factorize each of the following algebraic expression:
4x² + 12xy +9y²

Factorize each of the following algebraic expression:
9a² − 24ab + 16b²

Factorize each of the following algebraic expression:
p²q² − 6pqr + 9r²

Factorize each of the following algebraic expression:
36a² + 36a + 9

Factorize each of the following algebraic expression:
a² + 2ab + b² − 16

Factorize each of the following algebraic expression:
9z² − x² + 4xy − 4y²

Factorize each of the following algebraic expression:
9a⁴ − 24a²b² + 16b⁴ − 256

Factorize each of the following algebraic expression:
16 − a⁶ + 4a³b³ − 4b⁶

Factorize each of the following algebraic expression:
a² − 2ab + b² − c²

Factorize each of the following algebraic expression:
x² + 2x + 1 − 9y²

Factorize each of the following algebraic expression:
a² + 4ab + 3b²

Factorize each of the following algebraic expression:
96 − 4x − x²

Factorize each of the following algebraic expression:
a⁴ + 3a² +4

Factorize each of the following algebraic expression:
4x⁴ + 1

Factorize each of the following algebraic expression:
4x⁴ + y⁴

Factorize the following algebraic expression:
(x + 2)² − 6(x + 2) + 9

Factorize each of the following algebraic expression:
25 − p² − q² − 2pq

Factorize each of the following algebraic expressions:
x² + 9y² − 6xy − 25a²

Factorize each of the following algebraic expression:
49 − a² + 8ab − 16b²

Factorize each of the following algebraic expression:
a² − 8ab + 16b² − 25c²

Factorize each of the following algebraic expression:
x² − y² + 6y − 9

Factorize each of the following algebraic expression:
25x² − 10x + 1 − 36y²

Factorize each of the following algebraic expression:
a² − b² + 2bc − c²

Factorize each of the following algebraic expression:
a² + 2ab + b² − c²

Factorize each of the following algebraic expression:
49 − x² − y² + 2xy

Factorize each of the following algebraic expression:
a² + 4b² − 4ab − 4c²

Factorize each of the following algebraic expression:
x² − y² − 4xz + 4z²

Factorize each of the following algebraic expression:
x² + 12x − 45

Factorize each of the following algebraic expression:
40 + 3x − x²

Factorize each of the following algebraic expression:
a² + 3a − 88

Factorize each of the following algebraic expression:
a² − 14a − 51

Factorize each of the following algebraic expression:
x² − 22x + 120

Factorize each of the following algebraic expression:
x² − 11x − 42

Factorize each of the following algebraic expression:
a² + 2a − 3

Factorize each of the following algebraic expression:
a² + 14a + 48

Factorize each of the following algebraic expression:
y² + 5y − 36

Factorize each of the following algebraic expression:
(a + 7)(a − 10) + 16

Factorize each of the following quadratic polynomials by using the method of  completing the square:
p² + 6p + 8

Factorize each of the following quadratic polynomials by using the method of completing the square:
4y² + 12y + 5

Factorize each of the following quadratic polynomials by using the method of completing the square:
p² + 6p − 16

Factorize each of the following quadratic polynomials by using the method of completing the square:
x² + 12x + 20

Factorize each of the following quadratic polynomials by using the method of completing the square:
a² − 14a − 51

Factorize each of the following quadratic polynomials by using the method of completing the square:
a² + 2a − 3

Factorize each of the following quadratic polynomials by using the method of completing the square:
z² − 4z − 12