Clark Elliott
07/26/2023 · Senior High School
21. \( \left(x^{3}+2 x^{2}-x+1\right)\left(x^{2}+3 x+4\right) \)
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Step-by-step Solution
Calculate or simplify the expression \( (x^3+2x^2-x+1)(x^2+3x+4) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(x^{3}+2x^{2}-x+1\right)\left(x^{2}+3x+4\right)\)
- step1: Apply the distributive property:
\(x^{3}\times x^{2}+x^{3}\times 3x+x^{3}\times 4+2x^{2}\times x^{2}+2x^{2}\times 3x+2x^{2}\times 4-x\times x^{2}-x\times 3x-x\times 4+1\times x^{2}+1\times 3x+1\times 4\)
- step2: Multiply the terms:
\(x^{5}+3x^{4}+4x^{3}+2x^{4}+6x^{3}+8x^{2}-x^{3}-3x^{2}-4x+x^{2}+3x+4\)
- step3: Add the terms:
\(x^{5}+5x^{4}+9x^{3}+6x^{2}-x+4\)
La expresión \( \left(x^{3}+2 x^{2}-x+1\right)\left(x^{2}+3 x+4\right) \) simplificada es \( x^{5}+5x^{4}+9x^{3}+6x^{2}-x+4 \).
Quick Answer
La expresión simplificada es \( x^{5}+5x^{4}+9x^{3}+6x^{2}-x+4 \).
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