substitute $7c - 3$ for $l$ and $4c^2 + 5c$ for $w$ and simplify.

$\text{perimeter} = 2l + 2w$
$= 2(7c - 3) + 2(4c^2 + 5c)$
$= 14c - 6 + 8c^2 + 10c$
$= 8c^2 + 24c - 6$

part b

the agriculture club already has another solar panel with a surface area of $8c^2 + 16c - 11$.

once jessica completes the new chicken coop with its solar panels, what will be the total surface area of the solar panels the club owns?

$28c^3 + 15c^2 - 31c + 11$
$28c^3 + 31c^2 + c - 11$
$28c^3 + 23c^2 - 15c$
$59c^3 + c + 11$

Question

substitute $7c - 3$ for $l$ and $4c^2 + 5c$ for $w$ and simplify.

$\text{perimeter} = 2l + 2w$
$= 2(7c - 3) + 2(4c^2 + 5c)$
$= 14c - 6 + 8c^2 + 10c$
$= 8c^2 + 24c - 6$

part b

the agriculture club already has another solar panel with a surface area of $8c^2 + 16c - 11$.

once jessica completes the new chicken coop with its solar panels, what will be the total surface area of the solar panels the club owns?

$28c^3 + 15c^2 - 31c + 11$
$28c^3 + 31c^2 + c - 11$
$28c^3 + 23c^2 - 15c$
$59c^3 + c + 11$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Operations", "Like Terms" ], "new_concepts": [], "current_concepts": [ "Polynomial Operations", "Like Terms", "Algebraic Modeling" ] } ## Identify the given expressions $$ \begin{aligned} A_{\text{existing}} &= 8c^2 + 16c - 11 \ A_{\text{new}} &= l \times w = (7c - 3)(4c^2 + 5c) \end{aligned} $$ ## Expand the new surface area expression $$ \begin{aligned} A_{\text{new}} &= 7c(4c^2 + 5c) - 3(4c^2 + 5c) \ &= 28c^3 + 35c^2 - 12c^2 - 15c \ &= 28c^3 + 23c^2 - 15c \end{aligned} $$ ## Calculate the total surface area $$ \begin{aligned} A_{\text{total}} &= A_{\text{new}} + A_{\text{existing}} \ &= (28c^3 + 23c^2 - 15c) + (8c^2 + 16c - 11) \ &= 28c^3 + (23 + 8)c^2 + (-15 + 16)c - 11 \ &= 28c^3 + 31c^2 + c - 11 \end{aligned} $$

(A) $28c^3 + 15c^2 - 31c + 11$

(B) $28c^3 + 31c^2 + c - 11$

(C) $28c^3 + 23c^2 - 15c$

(D) $59c^3 + c + 11$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given expressions

Expand the new surface area expression

Calculate the total surface area

Answer: