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Answer
The product of the binomials is \( 4x^2 + 21x + 20 \).
Solution
1. Expand using the distributive property:
\[
(4x+5)(x+4) = 4x \cdot x + 4x \cdot 4 + 5 \cdot x + 5 \cdot 4
\]
2. Multiply each pair of terms:
\[
4x \cdot x = 4x^2
\]
\[
4x \cdot 4 = 16x
\]
\[
5 \cdot x = 5x
\]
\[
5 \cdot 4 = 20
\]
3. Combine like terms:
\[
4x^2 + 16x + 5x + 20 = 4x^2 + 21x + 20
\]
The product of the binomials is:
\[
4x^2 + 21x + 20
\]
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Simplify this solution The Deep Dive
To multiply the binomials \( (4x + 5)(x + 4) \), you can apply the distributive property, also known as the FOIL method (First, Outside, Inside, Last). First, multiply the first terms: \( 4x \cdot x = 4x^2 \). Next, multiply the outside terms: \( 4x \cdot 4 = 16x \). Then, multiply the inside terms: \( 5 \cdot x = 5x \). Finally, multiply the last terms: \( 5 \cdot 4 = 20 \). Now, combine all these results: \[ 4x^2 + 16x + 5x + 20 = 4x^2 + 21x + 20. \] So, the product of the binomials is: \[ (4x + 5)(x + 4) = 4x^2 + 21x + 20. \]
