Questions: 25v^2 + 40v + 16

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

Solution

Solution Steps

Step 1: Identify the Polynomial

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

Step 2: Factor the Polynomial

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

Step 3: Verify the Factorization

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

Final Answer

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

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