Question

factorise a.64x^3+8y^3. b.27x^y-xy^4. c.8x^3+8y^3+24x^2y+24xy^2. d.x^2+12x+27. e.x^2-19x+84

Answer 1

A.
$= {(4x)}^{3} + {(2y)}^{3} \\ = {64x}^{3} + {8y}^{3} + 3 \times 4x \times 2y(3x + 2y) \\ = {64x}^{3} + {8y}^{3} + {72x}^{2}y + 48x {y}^{2}$
C.
${(2x)}^{3} + {(2y)}^{3} + 3 \times 2x \times 2y(2x + 2y) \\ = {(2x + 2y)}^{3}$
D.
$= {x}^{2} +(9x + 3x) + 27 \\ = x(x + 9) + 3(x + 9) \\ =( x + 9)(x + 3)$
E.
$= {x}^{2} - 12x - 7x + 84 \\ = x(x - 12) - 7(x - 12) \\ = (x - 12)(x - 7)$