\(x^2 + 4x + 3)^2\

Question

\(x^2 + 4x + 3)^2\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Trinomial Squaring", "Polynomial Multiplication", "Polynomial Simplification" ], "new_concepts": [], "current_concepts": [ "Trinomial Squaring", "Polynomial Multiplication", "Polynomial Simplification" ] } ## Apply trinomial squaring formula Using the *Trinomial Squaring* knowledge point $$ (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca $$ $$ \begin{aligned} a &= x^2 \ b &= 4x \ c &= 3 \end{aligned} $$ ## Expand individual terms Using the *Polynomial Multiplication* knowledge point $$ \begin{aligned} a^2 &= (x^2)^2 = x^4 \ b^2 &= (4x)^2 = 16x^2 \ c^2 &= 3^2 = 9 \end{aligned} $$ ## Expand cross-product terms Using the *Polynomial Multiplication* knowledge point $$ \begin{aligned} 2ab &= 2(x^2)(4x) = 8x^3 \ 2bc &= 2(4x)(3) = 24x \ 2ca &= 2(3)(x^2) = 6x^2 \end{aligned} $$ ## Combine like terms Using the *Polynomial Simplification* knowledge point $$ \begin{aligned} (x^2 + 4x + 3)^2 &= x^4 + 16x^2 + 9 + 8x^3 + 24x + 6x^2 \ &= x^4 + 8x^3 + (16x^2 + 6x^2) + 24x + 9 \ &= x^4 + 8x^3 + 22x^2 + 24x + 9 \end{aligned} $$ $x^4 + 8x^3 + 22x^2 + 24x + 9$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Trinomial Squaring" ] }

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Question

Explanation:

Apply trinomial squaring formula

Expand individual terms

Expand cross-product terms

Combine like terms

Answer: