Question

Simplify ${(2x+5)}^2-{(2x-5)}^2$. (3 marks)

Answer 1

We know that ${(a+b)}^2$= $a^2$ + 2ab + $b^2$

and ${(a-b)}^2$ = $a^2$- 2ab + $b^2$ (1 mark)

${(2x+5)}^2$= ${\left(2x\right)}^2$ + 2 × 2x × 5 + $5^2$

= $4x^2$ + 20x +25 (0.5 mark)

${(2x-5)}^2$= ${\left(2x\right)}^2$- 2 × 2x × 5 + $5^2$

= ${4x}^2$- 20x + 25 (0.5 mark)

Therefore, ${(2x+5)}^2$ – ${(2x-5)}^2$

= ($4x^2$+ 20x + 25) - (${4x}^2$- 20x + 25)

= ($4x^2$+ 20x + 25 - ${4x}^2$+ 20x - 25)

=40x (1 mark)