1. $9(7q - 7) + (5q - 9)$
2. $3(5x + 3) + 8(3x + 6)$
3. $(-f - 9) + (-f - 9)$
4. $(4x + 7) + (9x + 2)$
5. $5(2b - 5) + (-6b + 5)$
6. $(9k - 3) + 4(7k + 6)$
7. $-7(-a - 7) + (9a + 5)$
8. $(-8z + 7) + (-z - 8)$
9. $4(8v + 4) + (6v + 6)$
10. $5(-6h - 8) + (-2h + 5)$

Question

Accepted Answer

{ "quality": "clear", "question_count": 10, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distributive Property", "Algebraic Simplification" ], "new_concepts": [], "current_concepts": [ "Distributive Property", "Algebraic Simplification", "Combining Like Terms" ] } ## Expand each expression using the distributive property $$ \begin{aligned} 1.&\quad 9(7q - 7) + (5q - 9) = 63q - 63 + 5q - 9\ 2.&\quad 3(5x + 3) + 8(3x + 6) = 15x + 9 + 24x + 48\ 3.&\quad (-f - 9) + (-f - 9) = -f - 9 - f - 9\ 4.&\quad (4x + 7) + (9x + 2) = 4x + 7 + 9x + 2\ 5.&\quad 5(2b - 5) + (-6b + 5) = 10b - 25 - 6b + 5\ 6.&\quad (9k - 3) + 4(7k + 6) = 9k - 3 + 28k + 24\ 7.&\quad -7(-a - 7) + (9a + 5) = 7a + 49 + 9a + 5\ 8.&\quad (-8z + 7) + (-z - 8) = -8z + 7 - z - 8\ 9.&\quad 4(8v + 4) + (6v + 6) = 32v + 16 + 6v + 6\ 10.&\quad 5(-6h - 8) + (-2h + 5) = -30h - 40 - 2h + 5 \end{aligned} $$ ## Combine like terms to simplify $$ \begin{aligned} 1.&\quad (63q + 5q) + (-63 - 9) = 68q - 72\ 2.&\quad (15x + 24x) + (9 + 48) = 39x + 57\ 3.&\quad (-f - f) + (-9 - 9) = -2f - 18\ 4.&\quad (4x + 9x) + (7 + 2) = 13x + 9\ 5.&\quad (10b - 6b) + (-25 + 5) = 4b - 20\ 6.&\quad (9k + 28k) + (-3 + 24) = 37k + 21\ 7.&\quad (7a + 9a) + (49 + 5) = 16a + 54\ 8.&\quad (-8z - z) + (7 - 8) = -9z - 1\ 9.&\quad (32v + 6v) + (16 + 6) = 38v + 22\ 10.&\quad (-30h - 2h) + (-40 + 5) = -32h - 35 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $9(7q - 7) + (5q - 9)$ | $68q - 72$ | | 2 | $3(5x + 3) + 8(3x + 6)$ | $39x + 57$ | | 3 | $(-f - 9) + (-f - 9)$ | $-2f - 18$ | | 4 | $(4x + 7) + (9x + 2)$ | $13x + 9$ | | 5 | $5(2b - 5) + (-6b + 5)$ | $4b - 20$ | | 6 | $(9k - 3) + 4(7k + 6)$ | $37k + 21$ | | 7 | $-7(-a - 7) + (9a + 5)$ | $16a + 54$ | | 8 | $(-8z + 7) + (-z - 8)$ | $-9z - 1$ | | 9 | $4(8v + 4) + (6v + 6)$ | $38v + 22$ | | 10 | $5(-6h - 8) + (-2h + 5)$ | $-32h - 35$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Algebraic Simplification" ] }

No.	Problem	Answer
2	\(3(5x + 3) + 8(3x + 6)\)	\(39x + 57\)
3	\((-f - 9) + (-f - 9)\)	\(-2f - 18\)
4	\((4x + 7) + (9x + 2)\)	\(13x + 9\)
5	\(5(2b - 5) + (-6b + 5)\)	\(4b - 20\)
6	\((9k - 3) + 4(7k + 6)\)	\(37k + 21\)
7	\(-7(-a - 7) + (9a + 5)\)	\(16a + 54\)
8	\((-8z + 7) + (-z - 8)\)	\(-9z - 1\)
9	\(4(8v + 4) + (6v + 6)\)	\(38v + 22\)
10	\(5(-6h - 8) + (-2h + 5)\)	\(-32h - 35\)

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QUESTION IMAGE

Question

Explanation:

Expand each expression using the distributive property

Combine like terms to simplify

Answer: