Question

Factorise:a) 250x³ - 432y³

b) x² + 3√3x - 30

URGENT!!!

Answer 1

(a)
Formula used: $a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2})$

[tex]250 x^{3} - 432 y^{3} \\ = 2 [125 x^{3} - 216 y^{3}] \\ = 2 [5^{3} x^{3} - 6^{3} y^{3}] \\ = 2 [(5x)^{3} - (6y)^{3}][/tex]

Now use the formula
[tex]=2 [(5x - 6y) (25 x^{2} + 30xy + 36 y^{2})] \\ =2(5x - 6y) (25 x^{2} + 30xy + 36 y^{2})[/tex]

(b)
$x^{2} + 3 \sqrt{3}x - 30 \\ = x^{2} - 2 \sqrt{3}x + 5\sqrt{3}x - 30\\ = x(x - 2 \sqrt{3}) + 5\sqrt{3}(x - 2 \sqrt{3}) \\ = (x - 2 \sqrt{3})(x + 5 \sqrt{3})$