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.
14pq, 28p2q2
Find the common factors of the terms.
2x, 3x2, 4
Find the common factors of the terms.
10pq, 20qr, 30rp
Factorise the following expression:
7x − 42
Factorise the following expression:
20 l2m + 30 alm
Factorise the following expression:
− 4a2 + 4ab − 4 ca
Factorise the following expression:
x2yz + xy2z + xyz2
Factorise.
15xy − 6x + 5y − 2
Factorise.
15pq + 15 + 9q + 25p
Factorize the following:
5x − 15x2
Factorize the following:
20x3 − 40x2 + 80x
Factorize the following:
10m3n2 + 15m4n − 20m2n3
Factorize the following:
9x2y + 3axy
Factorise by taking out the common factors :
2 (2x - 5y) (3x + 4y) - 6 (2x - 5y) (x - y)
Factorise:
`x^4 + y^4 - 27x^2y^2`
Factorise : (a2 - 3a) (a2 - 3a + 7) + 10
Factorise : 12(3x - 2y)2 - 3x + 2y - 1
Factorise : 2√3x2 + x - 5√3
Factorise : a3 - a2 +a
Factorise : a3b - a2b2 - b3
Factorise : 3x5y - 27x4y2 + 12x3y3
Factorise : 4x(3x - 2y) - 2y(3x - 2y)
Factorise: 36x2y2 - 30x3y3 + 48x3y2
factorise : m - 1 - (m-1)2 + am - a
Factorise: a4 - 625
Factorise the following by taking out the common factors:
(mx + ny)2 + (nx - my)2
Factorise the following by taking out the common factor
9x5y3 + 6x3y2 – 18x2y
