Question

factorise :
${8x}^{3} \: + {y}^{3}$
​

Answer 1

Step-by-step explanation:

$Explanation:</p><p></p><p>8x3+y3 is a sum of two cubes as it is equivalent to (2x)3+y3</p><p></p><p>Recall the identity a3+b3=(a+b)(a2−ab+b2)</p><p></p><p>Hence, 8x3+y3=(2x)3+y3</p><p></p><p>= (2x+y)((2x)2−(2x)y+y2)</p><p></p><p>= (2x+y)(4x2−2xy+y2)</p><p></p><p>Alternatively, 8x3+y3</p><p></p><p>= 8x3+4x2y−4x2y−2xy2+2xy2+y3</p><p></p><p>= 4x2(2x+y)−2xy(2x+y)+y2(2x+y)</p><p></p><p>= (2x+y)(4x2−2xy+y2)</p><p></p><p>$