Question

Factorise each of the following polynomial by regrouping.

a) x²y + xy² + xab + yab - y²z - xyz

b) pq² - aq² + pr² - ar² + pk² - ak²​

Answer 1

Answer:

Solution :-

a) x²y + xy² + xab + yab - y²z - xyz

➻ x²y + xy² + xab + yab - xyz - y²z

➻ xy(x + y) + ab(x + y) - yz(x + y)

➻ (x + y) (xy + ab - yz)

∴ The answer of this question is (x + y) (xy + ab - yz)

b) pq² - aq² + pr² - ar² + pk² - ak²

➻ q²(p - a) + r²(p - a) + k²(p - a)

➻ (p - a) (q² + r² + k²)

∴ The answer of this question is (p - a) (q² + r² + k²)

Answer 2

EVALUATION★

(a)

• (x²y + xy²) + (xab + yab) +( -y²z - xyz )

take common xy and and ab and -yz

• $= xy(x + y) + ab(x + y) - yz(x + y)$
• now common (x+y)

=$= (x + y)(xy + ab - yz)$

• _______________________________

(b)

• pq² - aq² + pr² - ar² + pk² - ak²

• take common q^2 , r^2 and k^2

• $= q {}^{2}(p - a) + r {}^{2}(p - a) + k {}^{2}(p - a)$
• now take common(p-a)

=$(p - a)(q {}^{2} + r {}^{2} + k {}^{2} )$

• _________________________________

I hope it helps you