using the distributive property

use the distributive property to match equivalent expressions.

$-7(-4 + x)$
$7(-4 - x)$
$7(4 + x)$
$-7(4 - x)$

$28 - 7x$
$28 + 7x$
$-28 - 7x$
$-28 + 7x$

Question

using the distributive property

use the distributive property to match equivalent expressions.

$-7(-4 + x)$
$7(-4 - x)$
$7(4 + x)$
$-7(4 - x)$

$28 - 7x$
$28 + 7x$
$-28 - 7x$
$-28 + 7x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Multiplication", "Polynomial Operations" ], "new_concepts": [ "Distributive Property" ], "current_concepts": [ "Distributive Property", "Polynomial Multiplication", "Polynomial Operations" ] } ## Expand the first expression $$ -7(-4 + x) = (-7)(-4) + (-7)(x) = 28 - 7x $$ ## Expand the second expression $$ 7(-4 - x) = 7(-4) + 7(-x) = -28 - 7x $$ ## Expand the third and fourth expressions $$ \begin{aligned} 7(4 + x) &= 7(4) + 7(x) = 28 + 7x\ -7(4 - x) &= -7(4) - 7(-x) = -28 + 7x \end{aligned} $$ - $-7(-4 + x)$ matches $28 - 7x$ - $7(-4 - x)$ matches $-28 - 7x$ - $7(4 + x)$ matches $28 + 7x$ - $-7(4 - x)$ matches $-28 + 7x$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Distributive Property" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the first expression

Expand the second expression

Expand the third and fourth expressions

Answer: