Advertisements
Advertisements
Question
Factorise the following by taking out the common factors:
(mx + ny)2 + (nx - my)2
Advertisements
Solution
(mx + ny)2 + (nx - my)2
= m2x2 + n2y2 + 2mnxy + n2x2 + m2y2 - 2mnxy
= m2x2 + n2y2 + n2x2 + m2y2
= m2x2 + n2x2 + m2y2 + n2y2
= x2(m2 + n2) + y2(m2 + n2)
Here, the common factor is (m2 + n2).
Dividing throughout by (m2 + n2), we get
`(x^2("m"^2 + "n"^2))/(("m"^2 + "n"^2)) + (y^2("m"^2 + "n"^2))/(("m"^2 + "n"^2)`
= x2 + y2
∴ (mx + ny)2 + (nx - my)2
= (m2 + n2)(x2 + y2).
APPEARS IN
RELATED QUESTIONS
Factorise the following expression:
−16z + 20z3
Factorise.
ax + bx − ay − by
Factorise.
15pq + 15 + 9q + 25p
Factorize the following:
3x − 9
Factorize the following:
20x3 − 40x2 + 80x
Factorize the following:
10m3n2 + 15m4n − 20m2n3
Factorize the following:
a4b − 3a2b2 − 6ab3
Factorize the following:
16m − 4m2
Factorize the following:
−4a2 + 4ab − 4ca
Factorise : `(9a)^2 + 1/(9a)^2 - 2 - 12a + 4/(3a)`
Factorise : a - b - 4a2 + 4b2
Factorise: x4 + y4 - 3x2y2
Factorise : 9x 2 + 3x - 8y - 64y2
Factorise : 2√3x2 + x - 5√3
Factorise : `1/4 ( a + b )^2 - 9/16 ( 2a - b )^2`
Find the value of : ( 67.8 )2 - ( 32.2 )2
Find the value of : `[(6.7)^2 - (3.3)^2]/[6.7 - 3.3]`
Factorise : 15x + 5
Factorise : 2x3b2 - 4x5b4
Factorise : a3b - a2b2 - b3
factorise : 8(2a + 3b)3 - 12(2a + 3b)2
Factorise:
a2 – ab(1 – b) – b3
Factorise the following by taking out the common factors:
24m4n6 + 56m6n4 - 72m2n2
Factorise the following by taking out the common factors:
(a - b)2 -2(a - b)
Factorise the following by taking out the common factors:
2a(p2 + q2) + 4b(p2 + q2)
Factorise the following by taking out the common factors:
81(p + q)2 -9p - 9q
Factorise:
`4"a"^2 + (1)/(4"a"^2) - 2 - 6"a" + (3)/(2"a")`
