Question

please factorise it..........asap

Answer 1

To factorise:x³+6x²+12x+16
${x}^{3} + {6x}^{2} + 12x + 8 + 8 \\ = {x}^{3} + {6x}^{2} + 12x + {2}^{3} + {2}^{3} \\ = {x}^{3} + 3 \times {x}^{2} \times 2 + 3 \times x \times {2}^{2} + {2}^{3} + {2}^{3} \\ = {(x + 2)}^{3} + {2}^{3} \\ = {(x + 2 + 2)}^{3} - 3 \times (x + 2)(2)(x + 2 + 2) \\ = {(x + 4)}^{3} - 6(x + 2)(x + 4) \\ = {(x + 4)}^{3}(1 - 6(x + 2)) \\ = {(x + 4)}^{3} ( - 6x - 11)$
or
${-(x+4)}^{3}(6x+11)$