Question
6. Multiply: \( (x+3)\left(4 x^{2}+6 x+8\right) \)
Ask by George Bird. in the United States
Feb 05,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The result is \( 4x^{3}+18x^{2}+26x+24 \).
Solution
Calculate or simplify the expression \( (x+3)(4x^2+6x+8) \).
Calculate or simplify the expression \( (x+3)(4x^2+6x+8) \).
Simplify the expression by following steps:
- step0: Multiply the terms:
\(\left(x+3\right)\left(4x^{2}+6x+8\right)\)
- step1: Apply the distributive property:
\(x\times 4x^{2}+x\times 6x+x\times 8+3\times 4x^{2}+3\times 6x+3\times 8\)
- step2: Multiply the terms:
\(4x^{3}+6x^{2}+8x+12x^{2}+18x+24\)
- step3: Add the terms:
\(4x^{3}+18x^{2}+26x+24\)
The result of multiplying \( (x+3) \) by \( (4x^{2}+6x+8) \) is \( 4x^{3}+18x^{2}+26x+24 \).
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Simplify this solution Mind Expander
To solve the multiplication \( (x + 3)(4x^2 + 6x + 8) \), we can use the distributive property, also known as the FOIL method. We distribute \( (x + 3) \) to each term inside the parentheses: 1. \( x \times 4x^2 = 4x^3 \) 2. \( x \times 6x = 6x^2 \) 3. \( x \times 8 = 8x \) Now for the \( 3 \): 4. \( 3 \times 4x^2 = 12x^2 \) 5. \( 3 \times 6x = 18x \) 6. \( 3 \times 8 = 24 \) Now we combine all these terms: \[ 4x^3 + 6x^2 + 8x + 12x^2 + 18x + 24 \] Combine like terms: - For \( x^2 \): \( 6x^2 + 12x^2 = 18x^2 \) - For \( x \): \( 8x + 18x = 26x \) Thus, we get: \[ 4x^3 + 18x^2 + 26x + 24 \] So the final answer is: \( \boxed{4x^3 + 18x^2 + 26x + 24} \)
