Mathematics 10 — Exercise 4.1 · Q2 (ii)

Full question

For the following functions, find gf.

Step-by-step solution

1. Substitute the function expressions, keeping the brackets.

   $$\left(x+2\right)\times \left(2\times x+4\right)$$

2. Distribute each bracket product: each term multiplies every term in the other bracket.

   $$2\times x^2+8\times x+8$$

3. Write EVERY distributed product before collecting terms.

   $$4\times 2+4\times x+2\times \left(2\times x\right)+x\times \left(2\times x\right)$$

4. Calculate this individual product, including its sign and powers.

   $$4\times 2=8$$

5. Calculate this individual product, including its sign and powers.

   $$4\times x=4\times x$$

6. Calculate this individual product, including its sign and powers.

   $$2\times \left(2\times x\right)=4\times x$$

7. Calculate this individual product, including its sign and powers.

   $$x\times \left(2\times x\right)=2\times x^2$$

8. These terms have the same variable part. Add ONLY their coefficients.

   $$8=8$$

9. These terms have the same variable part. Add ONLY their coefficients.

   $$4+4=8$$

10. These terms have the same variable part. Add ONLY their coefficients.

    $$2=2$$

11. Put the simplified groups together.

    $$8+8\times x+2\times x^2$$

12. Collect terms with the same power and simplify their coefficients.

    $$2\times x^2+8\times x+8$$

Answer

The final answer is shown below.