Factor. 4u^2 + 20u + 25 ______

Identify a, b, c: Identify a, b, and c in the quadratic expression 4u^2 + 20u + 25. Compare 4u^2 + 20u + 25 with ax^2 + bx + c. a = 4 b = 20 c = 25Find two numbers: Find two numbers whose product is a*c (4*25 = 100) and whose sum is b (20). We need to find two numbers that multiply to 100 and add up to 20. 10 * 10 = 100 10 + 10 = 20 Two numbers: 10, 10Write quadratic expression: Write the quadratic expression using the two numbers found in Step 2. 4u^2 + 20u + 25 can be written as 4u^2 + 10u + 10u + 25.Factor by grouping: Factor by grouping. Group the terms: (4u^2 + 10u) + (10u + 25). Factor out the common factors from each group. 2u(2u + 5) + 5(2u + 5).Factor common binomial: Factor out the common binomial factor. The common binomial factor is (2u + 5). The factored form is (2u + 5)(2u + 5) or (2u + 5)^2.

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Q. Factor.

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4u^2 + 20u + 25

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $4u^2 + 20u + 25$ . Compare $4u^2 + 20u + 25$ with $ax^2 + bx + c$ . $a = 4$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $4*25 = 100$ ) and whose sum is $b$ ( $20$ ). $\newline$ We need to find two numbers that multiply to $100$ and add up to $20$ . $\newline$ $10 * 10 = 100$ $\newline$ $10 + 10 = 20$ $\newline$ Two numbers: $10$ , $10$
Write quadratic expression: Write the quadratic expression using the two numbers found in Step $2$ . $\newline$ $4u^2 + 20u + 25$ can be written as $4u^2 + 10u + 10u + 25$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $(4u^2 + 10u) + (10u + 25)$ . $\newline$ Factor out the common factors from each group. $\newline$ $2u(2u + 5) + 5(2u + 5)$ .
Factor common binomial: Factor out the common binomial factor. $\newline$ The common binomial factor is $(2u + 5)$ . $\newline$ The factored form is $(2u + 5)(2u + 5)$ or $(2u + 5)^2$ .