Question

Factorise the following by regrouping the terms.
a) 6xy-y^2+12xz-2yz
b) b^2-ab(1-a)-a^3
c) a^2-a(x+2y)+2xy
d) x^3-2x^2y+3xy^2-6y^3
e) xy(a^2+1)-a(x^2+y^2)​

Answer 1

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).

Answer 2

$\huge{\orange{\underline{\purple{\mathscr{Solution}}}}}$

Michael was shocked by the news of the miracle recovery for he thought that Sebastian Shultz couldn’t be the boy he had met. Six weeks ago he was badly injured in a motorway accident, his condition in the hospital was described as critical though stable. Sebastian didn’t regain consciousness. His parents were informed that the boy was in a coma.