Question

Which expression In factored form is equivalent to this expression?
4(x²- 2x) – 2(x²– 3)

Answer 1

To factor the expression 4(x²- 2x) – 2(x²– 3), distribute the coefficients, combine like terms, and factor the resulting quadratic equation to obtain 2(x - 1)(x - 3).

Step-by-step explanation:

The student has asked how to write a given algebraic expression in a factored form. The expression to be factored is 4(x²- 2x) – 2(x²– 3). To factor this expression, we perform the following steps:

1. Distribute the coefficients by multiplying by the terms inside the parentheses: 4x² - 8x - 2x² + 6.
2. Combine like terms: (4x² - 2x²) - 8x + 6 = 2x² - 8x + 6.
3. Factor the quadratic equation: 2(x - 1)(x - 3).

Therefore, the expression in factored form equivalent to 4(x²- 2x) – 2(x²– 3) is 2(x - 1)(x - 3).