Question

4. Factorise the following by using the
identities or regrouping the terms.
a) 2x2 – 32x + 128 b) 3x2 + 18x + 27
c) 12x3y2 + 24x?y2 d) 36x3y22 +48x2y32
e) x2 + 7x + 12 f) 8r3 – 343
g) x2 – 2xy + y2 – x+y
h) x4 + 22x3 + 121x?'
i) a2 + b2 – 2(ab – ac + bc)​

Answer 1

Q4.(a)

  $2x^{2} -32x +128 \\=2(x^{2} -16x+64\\=2(x^{2} -(4+12)x +64) \\= 2(x^{2} -4-12x+64)\\= 2(x(x-4)-12(x-4))\\=2(x-4)(x-12)$

(b)

$3x^2 +18x +27\\= 3(x^{2}+6x+9)\\=3(x^2+ 3x+3x +9)\\=3(x+3)(x+3)$

(c)

$12x^3y^2 +24xy^2 \\=12xy^2(x^2+1)\\=12xy^2(x+1) (x-1)$

(d )question not clearly given

(e)

$x^2 +7x +12\\=x^2 +3x+4x+12\\=x(x+3)+4(x+3)\\=(x+4)(x+3)$

(f)

$8r^3 -343 \\= (2r-7)^3$

(g) Simplest form already

$x^2 -2xy +y^2 -x+y$

(h) $x(x^2+22x^2+121)$

(i)$a^2+b^2 -2ab -2ac-2bc$