Questions: 25v^2 + 40v + 16

25v^2 + 40v + 16
Transcript text: \[ 25 v^{2}+40 v+16 \]
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Solution

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Solution Steps

Step 1: Identify the Polynomial

We start with the polynomial expression: 25v2+40v+16 25 v^{2} + 40 v + 16

Step 2: Factor the Polynomial

To factor the polynomial, we look for two identical binomials. The expression can be rewritten as: (5v+4)2 (5v + 4)^{2}

Step 3: Verify the Factorization

To ensure the factorization is correct, we can expand (5v+4)2(5v + 4)^{2}: (5v+4)(5v+4)=25v2+20v+20v+16=25v2+40v+16 (5v + 4)(5v + 4) = 25v^{2} + 20v + 20v + 16 = 25v^{2} + 40v + 16 This confirms that the factorization is accurate.

Final Answer

(5v+4)2\boxed{(5v + 4)^{2}}

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