Factor. 25q^2 - 20q + 4 ______

Identify Perfect Square Trinomial: Identify if the quadratic is a perfect square trinomial. 25q^2 = (5q)^2, 4 = 2^2, and 20q = 2 * 5q * 2. Check if it fits the form (a - b)^2 = a^2 - 2ab + b^2.Write in Form: Write the expression in the form of a perfect square trinomial. 25q^2 - 20q + 4 = (5q)^2 - 2 * 5q * 2 + 2^2.Factor Trinomial: Factor the perfect square trinomial. (5q)^2 - 2 * 5q * 2 + 2^2 = (5q - 2)^2.Check Factored Form: Check the factored form by expanding it to ensure it matches the original expression. (5q - 2)(5q - 2) = 25q^2 - 10q - 10q + 4 = 25q^2 - 20q + 4.

Home

Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor.

\newline

25q^2 - 20q + 4

Identify Perfect Square Trinomial: Identify if the quadratic is a perfect square trinomial. $25q^2 = (5q)^2$ , $4 = 2^2$ , and $20q = 2 \times 5q \times 2$ . Check if it fits the form $(a - b)^2 = a^2 - 2ab + b^2$ .
Write in Form: Write the expression in the form of a perfect square trinomial. $\newline$ $25q^2 - 20q + 4 = (5q)^2 - 2 \times 5q \times 2 + 2^2$ .
Factor Trinomial: Factor the perfect square trinomial. $\newline$ $(5q)^2 - 2 \times 5q \times 2 + 2^2 = (5q - 2)^2$ .
Check Factored Form: Check the factored form by expanding it to ensure it matches the original expression. $\newline$ $(5q - 2)(5q - 2) = 25q^2 - 10q - 10q + 4 = 25q^2 - 20q + 4$ .