Question

Which expression in factored form is equivalent to this expression? 4(x^2 - 2x) - 2(x^2 - 3)

A) (2x - 3)(x + 1)
B) (2x + 3)(8 + 1)
C) 2(+ 1)(+ + 3)
D) 2(67 - 1)(1 – 3)

Answer 1

The equivalent expression in factored form is 2(x - 1)(x - 3).

Step-by-step explanation:

To find the expression in factored form that is equivalent to 4(x^2 - 2x) - 2(x^2 - 3), we can simplify and factor out common terms. First, distribute the 4 and the -2 to the terms inside the brackets:

4(x^2 - 2x) - 2(x^2 - 3) = 4x^2 - 8x - 2x^2 + 6

Combine like terms:

2x^2 - 8x + 6

Now, we need to factor this quadratic expression:

2(x^2 - 4x + 3)

Finally, factor the quadratic binomial:

2(x - 1)(x - 3)

So the equivalent expression in factored form is 2(x - 1)(x - 3).