15.4 Identities and equivalent expressions — Practise

1. Expand $(x+4)^2$.

Answer: $x^2+8x+16$

2. Expand $(x+3)(x+5)$.

Answer: $x^2+8x+15$

3. Write $x^2+7x+12$ as a product of two brackets.

Answer: $(x+3)(x+4)$

4. Simplify $3x+5+2x-7$.

Answer: $5x-2$

5. Find $k$ if $(x+2)(x+k)\equiv x^2+7x+10$.

Answer: $k=5$

6. Find $a$ if $3(x+2)\equiv ax+6$.

Answer: $a=3$

7. For $x=3$, evaluate both $2(x+4)$ and $2x+8$.

Answer: $14$ for each

8. Complete the identity: $(x-5)^2\equiv x^2+bx+c$.

Answer: $b=-10$, $c=25$

9. Write $4x+12$ as a product.

Answer: $4(x+3)$

10. Expand $(x-2)(x+2)$ and state the equivalent expression.

Answer: $x^2-4$