Advertisements
Advertisements
Question
Factorise the following by taking out the common factors:
p(p2 + q2 - r2) + q(r2 - q2 -p2) - r(p2 + q2 - r2)
Advertisements
Solution
p(p2 + q2 - r2) + q(r2 - q2 - p2) - r(p2 + q2 - r2)
= p(p2 + q2 - r2) - q(-r2 + q2 + p2) - r(p2 + q2 - r2)
= p(p2 + q2 - r2) - q(p2 + q2 - r2) - r(p2 + q2 - r2)
Here, the common factor is (p2 + q2 - r2).
Dividing throughout by (p2 + q2 - r2)
`("p"("p"^2 + "q"^2 - "r"^2))/("p"^2 + "q"^2 - "r"^2) - ("q"("p"^2 + "q"^2 - "r"^2))/(("p"^2 + "q"^2 - "r"^2)) - ("r"("p"^2 + "q"^2 - "r"^2))/(("p"^2 + "q"^2 - "r"^2))`
= p - q - r
∴ p(p2 + q2 - r2) + q(r2 - q2 - p2) - r(p2 + q2 - r2)
= (p2 + q2 - r2)(p - q - r).
APPEARS IN
RELATED QUESTIONS
Find the common factors of the terms.
12x, 36
Find the common factors of the terms.
2x, 3x2, 4
Find the common factors of the terms.
16x3, −4x2, 32x
Factorise the following expression:
− 4a2 + 4ab − 4 ca
Factorise.
x2 + xy + 8x + 8y
Factorise.
ax + bx − ay − by
Factorise by taking out the common factors :
2 (2x - 5y) (3x + 4y) - 6 (2x - 5y) (x - y)
Factories by taking out common factors :
ab(a2 + b2 - c2) - bc(c2 - a2 - b2) + ca(a2 + b2 - c2)
Factories by taking out common factors :
2x(a - b) + 3y(5a - 5b) + 4z(2b - 2a)
Factorise:
`x^4 + y^4 - 27x^2y^2`
Factorise : 4x4 + 9y4 + 11x2y2
Factorise : `x^2 + 1/x^2 - 3`
Factorise:
(2a - 3)2 - 2 (2a - 3) (a - 1) + (a - 1)2
Factorise:
5a2 - b2 - 4ab + 7a - 7b
Factorise : 12(3x - 2y)2 - 3x + 2y - 1
Factorise : `1/4 ( a + b )^2 - 9/16 ( 2a - b )^2`
Factorise : 17a6b8 - 34a4b6 + 51a2b4
Factorise : 2b (2a + b) - 3c (2a + b)
Factorise : (a+ 2b) (3a + b) - (a+ b) (a+ 2b) +(a+ 2b)2
Factorise: 36x2y2 - 30x3y3 + 48x3y2
factorise : a2 - ab - 3a + 3b
factorise : x2y - xy2 + 5x - 5y
Factorise xy2 - xz2, Hence, find the value of :
9 x 82 - 9 x 22
Factorise xy2 - xz2, Hence, find the value of :
40 x 5.52 - 40 x 4.52
Factorise the following by taking out the common factors:
4x2y3 - 6x3y2 - 12xy2
