Mathematics 10 — Exercise 2.1 · Q1 (ii)

Full question

Write the following quadratic equation in standard form: 2 × x × (x+1) = 4 × (2 × x+3).

Step-by-step solution

1. Substitute the function expressions, keeping the brackets.

   $$2\times x\times \left(x+1\right)-8\times x+12$$

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

   $$2\times x^2-6\times x-12$$

3. Write EVERY distributed product before collecting terms.

   $$2\times 1\times x+2\times xx-12-8\times x$$

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

   $$2\times 1\times x=2\times x$$

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

   $$2\times xx=2\times x^2$$

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

   $$\left(-1\right)\times 12=-12$$

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

   $$-8\times x=-8\times x$$

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

   $$2-8=-6$$

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

   $$2=2$$

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

    $$-12=-12$$

11. Put the simplified groups together.

    $$-6\times x+2\times x^2-12$$

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

    $$2\times x^2-6\times x-12$$

13. Expand the brackets and subtract the right-hand terms from both sides. Collect powers of the variable.

    $$2\times x^2-6\times x-12=0$$

Answer

The final answer is shown below.