Question

Which of the following is a factor of (x+y)^3-(x^3+y^3)?

A)x^2+y^2+2xy
B)x^2+y^2-xy
C)xy^2
D)3xy​

Answer 1

Answer:

D is the correct option

Answer 2

Answer:

Question :-

Factorise the following by regrouping the terms.

a) 6xy  - y² + 12xz - 2yz

b) b² - ab(1 - a) - a³

c) a² - a(x + 2y) + 2xy

d) x³ - 2x²y + 3xy² - 6y³

e) xy(a² + 1)-a(x² + y²)

Solution :-

a) $\sf{6xy-y^2+12xz-2yz}$

$\sf{= y(6x-y)+2z(6x-y) }$

$\sf{= (6x-y)(y+2z)}$

◘ The factorised form is (6x - y)(y + 2z).

_________________

b) $\sf{ b^2-ab(1-a)-a^3}$

$\sf{=b^2-ab+a^2b-a^3 }$

$\sf{=b(b-a)+a^2(b-a)}$

$\sf{=(b-a)(b+a^2)}$

◘ The factorised form is (b - a)(b + a²).

_________________

c) $\sf{a^2-a(x+2y)+2xy}$

$\sf{=a^2-ax-2ay+2xy }$

$\sf{= a(a-x)-2y(a-x)}$

$\sf{= (a-x)(a-2y)}$

◘ The factorised form is (a - x)(a - 2y).

_________________

d) $\sf{x^3-2x^2y+3xy^2-6y^3}$

$\sf{=x^2(x-2y)+3y^2(x-2y) }$

$\sf{= (x-2y)(x^2+3y^2)}$

◘ The factorised form is (x - 2y)(x² + 3y²).

_________________

e) $\sf{xy(a^2+1)-a(x^2+y^2)}$

$\sf{= a^2xy+xy-ax^2-ay^2}$

$\sf{=a^2xy - ax^2 + xy - ay^2}$

$\sf{=ax(ay-x)-y(ay-x)}$

$\sf{=( ax - y )( ay - x )}$

◘ The factorised form is (ax - y)(ay - x).