1. $(x + 4)(x + 7)$

2. $(x - 3)(x + 5)$

3. $(2y + 1)(y + 6)$

Question

1. $(x + 4)(x + 7)$

2. $(x - 3)(x + 5)$

3. $(2y + 1)(y + 6)$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "FOIL Method", "Polynomial Multiplication" ], "current_concepts": [ "FOIL Method", "Polynomial Multiplication", "Distributive Property" ] } ## Expand the first expression $$ \begin{aligned} (x+4)(x+7) &= x(x) + x(7) + 4(x) + 4(7) \ &= x^2 + 7x + 4x + 28 \ &= x^2 + 11x + 28 \end{aligned} $$ ## Expand the second expression $$ \begin{aligned} (x-3)(x+5) &= x(x) + x(5) - 3(x) - 3(5) \ &= x^2 + 5x - 3x - 15 \ &= x^2 + 2x - 15 \end{aligned} $$ ## Expand the third expression $$ \begin{aligned} (2y+1)(y+6) &= 2y(y) + 2y(6) + 1(y) + 1(6) \ &= 2y^2 + 12y + y + 6 \ &= 2y^2 + 13y + 6 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $(x+4)(x+7)$ | $x^2 + 11x + 28$ | | 2 | $(x-3)(x+5)$ | $x^2 + 2x - 15$ | | 3 | $(2y+1)(y+6)$ | $2y^2 + 13y + 6$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Multiplication" ] }

No.	Problem	Answer
2	\((x-3)(x+5)\)	\(x^2 + 2x - 15\)
3	\((2y+1)(y+6)\)	\(2y^2 + 13y + 6\)

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QUESTION IMAGE

Question

Explanation:

Expand the first expression

Expand the second expression

Expand the third expression

Answer: