Mathematics 10 — Exercise Review · Q2 (ii)

Full question

For the following functions, find f-g.

Step-by-step solution

1. Substitute the function expressions, keeping the brackets.

   $$-(x^2-25)-(x+5)$$

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

   $$-x^2-x+20$$

3. Write EVERY distributed product before collecting terms.

   $$25-x^2-5-x$$

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

   $$25=25$$

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

   $$-x^2=-x^2$$

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

   $$\left(-1\right)\times 5=-5$$

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

   $$-x=-x$$

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

   $$25-5=20$$

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

   $$-1=-1$$

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

    $$-1=-1$$

11. Put the simplified groups together.

    $$20-x^2-x$$

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

    $$-x^2-x+20$$

Answer

The final answer is shown below.