simplifying polynomial expressions

$a$, $b$, and $c$ are polynomials, where:
$a = 3x - 4$
$b = x + 7$
$c = x^2 + 2$

what is $a^2 - (b + c)$ in simplest form?

$8x^2 - 25x + 7$
$8x^2 - 25x + 11$
$10x^2 - 25x + 7$
$10x^2 - 25x + 11$

Question

simplifying polynomial expressions

$a$, $b$, and $c$ are polynomials, where:
$a = 3x - 4$
$b = x + 7$
$c = x^2 + 2$

what is $a^2 - (b + c)$ in simplest form?

$8x^2 - 25x + 7$
$8x^2 - 25x + 11$
$10x^2 - 25x + 7$
$10x^2 - 25x + 11$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Multiplication", "Polynomial Addition", "Polynomial Subtraction" ], "new_concepts": [], "current_concepts": [ "Polynomial Operations", "Polynomial Multiplication", "Polynomial Addition", "Polynomial Subtraction" ] } ## Expand the term $A^2$ $$ \begin{aligned} A^2 &= (3x - 4)^2 \ &= (3x)^2 - 2(3x)(4) + (-4)^2 \ &= 9x^2 - 24x + 16 \end{aligned} $$ ## Simplify the term $(B + C)$ $$ \begin{aligned} B + C &= (x + 7) + (x^2 + 2) \ &= x^2 + x + 9 \end{aligned} $$ ## Subtract $(B + C)$ from $A^2$ $$ \begin{aligned} A^2 - (B + C) &= (9x^2 - 24x + 16) - (x^2 + x + 9) \ &= 9x^2 - 24x + 16 - x^2 - x - 9 \ &= (9x^2 - x^2) + (-24x - x) + (16 - 9) \ &= 8x^2 - 25x + 7 \end{aligned} $$

(A) $8x^2 - 25x + 7$

(B) $8x^2 - 25x + 11$

(C) $10x^2 - 25x + 7$

(D) $10x^2 - 25x + 11$

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

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QUESTION IMAGE

Question

Explanation:

Expand the term \(A^2\)

Simplify the term \((B + C)\)

Subtract \((B + C)\) from \(A^2\)

Answer: