Question

Factorise the following
(a) x²+y-xy-x
(b) a³-8b³+1+6ab
(c) a²+2ab+b²-9c²
(d) m²+17mn-84n²
(e) 4x²+9y²+16z²+12xy-24yz-16xz
(g) x²-y²+4y-4

Answer 1

(a).x²+y-xy-x
=> x²-x-xy+y
=>x(x-1)-y(x-1)
=>(x-y)(x-1) Ans.


b)a³-8b³+1+6ab
=>(a)³+(-2b)³+(1)^3-(3*a*-2b*1)
=>(a-2b+1)(a²+4b²+1+2ab+2b-a) Ans.


(c).a²+2ab+b²-9c²
=> (a)²+(2×a×b)+(b)²-(3c)²
=>(a+b)²-(3c)²
=>(a+b+c)(a+b-c) Ans.

d) m²+17mn-84n²
=>m²+21mn-4mn-84n²
=>m(m+21n)-4n(m+21n)
=>(m-4n)(m+21n) Ans.

e) 4x²+9y²+16z²+12xy-24yz-16xz
=>(2x)²+(3y)²+(-4z)²+(2*2x*3y)+(2*3y*-4z)+(2*2x*-4z)
=>(2x+3y-4z)²
=>(2x+3y-4z)(2x+3y-4z) Ans.

(g).x²-y²+4y-4
=>x²-(y²-4y+4)
=>x²-(y-2)²
=>(x-y+2)(x+y-2) Ans.