Question

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

Answer 1

To find the factored form equivalent of the expression 4(x^2-2x)-2(x^2-3), first, expand and combine like terms. Then factor by finding two numbers that multiply to the product of the quadratic term coefficient and constant term and add to the linear coefficient. The factored form is 2(x - 3)(x - 1).

Step-by-step explanation:

The student has asked to find the factored form equivalent of the expression 4(x^2-2x)-2(x^2-3). To solve this, we need to first expand the expression:

• 4x^2 - 8x - 2x^2 + 6

Then, combine like terms:

• (4x^2 - 2x^2) - 8x + 6
• 2x^2 - 8x + 6

Now we look for a factored form by finding two numbers that multiply to 12 (2•6) and add to -8. Those numbers are -2 and -6.

The expression can be factored as:

• 2(x - 3)(x - 1)

This is the factored form equivalent of the original expression.