multiply.

$(5u - 6v)(5u + 6v)$

simplify your answer.

Question

multiply.

$(5u - 6v)(5u + 6v)$

simplify your answer.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Polynomial Expansion", "FOIL Method" ], "new_concepts": [ "Difference of Squares" ], "current_concepts": [ "Polynomial Expansion", "FOIL Method", "Difference of Squares" ] } ## Identify the algebraic structure Using the *Polynomial Expansion* and *FOIL Method* knowledge points $$ (5u - 6v)(5u + 6v) $$ ## Apply the FOIL method Using the *FOIL Method* knowledge point $$ \begin{aligned} (5u - 6v)(5u + 6v) &= (5u)(5u) + (5u)(6v) + (-6v)(5u) + (-6v)(6v) \ &= 25u^2 + 30uv - 30uv - 36v^2 \end{aligned} $$ ## Combine like terms Using the *Polynomial Expansion* knowledge point $$ \begin{aligned} 25u^2 + 30uv - 30uv - 36v^2 &= 25u^2 + 0uv - 36v^2 \ &= 25u^2 - 36v^2 \end{aligned} $$ Multiply. $$(5u - 6v)(5u + 6v)$$ Simplify your answer. $25u^2 - 36v^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Difference of Squares" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the algebraic structure

Apply the FOIL method

Combine like terms

Answer: