Question

Factorise the expressions. (i) `ax^2 + bx` (ii) `7p^2 + 21q^2` (iii) `2x^3 + 2xy^2 + 2xz^2` (iv) `am^2 + bm^2 + bn^2 + an^2` (v) `(lm + l) + m +1` (vi) `y(y+z) + 9(y+z)` (vii) `5y^2 - 20y - 8z + 2yz` (viii) `10ab + 4a + 5b +2` (ix) `6xy - 4y + 6 - 9x`

Answer 1

(i) `ax^2 + bx`
`x(ax+b)`
(ii) `7p^2+ 21q^2`
`= 7(p^2 + 3q^2)`
(iii) `2x^3 + 2xy^2 + 2xz^2`
`2x(x^2 + y^2 + z^2)`
(iv) `am^2 + bm^2 + bn^2 + an^2`
`a(m^2+n^2)+ b(m^2+n^2)`
`(a+b)(m^2+ n^2)`
(v) `(lm+l)+m+l`
= `lm+l+m+l`
`= l(m+1)+1(m+1)`
`= (l+1)(m+1)`
(vi) `y(y+z)+ 9(y+z)`
`(y+9)(y+z)`
(vii)`5y^2 - 20y- 8z + 2yz`
`= 5y(y- 4) + 2z(y-4)`
`= (5y+2z)(y-4)`
(viii) `10ab +4a +5b+2`
`= 2a(5b+2)+1(5b+2)`
`=(2a+1)(5b+2)`
(ix) `6xy-4y+6-9x`
`= 2y(3x -2)-3(3x-2)`
`=(2y-3)(3x-2)`
answer