Question

Factor the expression. $$7 x^{2}-28 x+28$$

Short answer

The factored form of the expression \(7x^{2}-28x+28\) is \(7(x-2)^{2}\).

Step-by-step solution

Identify Common Factors

The expression is \(7x^{2}-28x+28\). All the coefficients here (7, -28, and 28) have a common factor, which is 7.

Factor Out the Common Factor

When you factor out 7 from each term in the expression, you get \(7(x^{2}-4x+4)\).

Factor the Quadratic Expression

The expression inside the parentheses, \(x^{2}-4x+4\), is a quadratic expression. It can be factored using the formula \(x^{2}-2abx+a^{2} = (x-a)^{2}\), where a is 2 in this case. It factors to \((x-2)^{2}\).