find the product.
$(3a^4 + 4)^2$

$6a^4 + 8$
$9a^8 + 16$
$9a^8 + 24a^4 + 16$
$9a^{16} + 24a^4 + 16$

Question

find the product.
$(3a^4 + 4)^2$

$6a^4 + 8$
$9a^8 + 16$
$9a^8 + 24a^4 + 16$
$9a^{16} + 24a^4 + 16$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Multiplying Binomials", "Product of Powers" ], "new_concepts": [ "Square of a Binomial" ], "current_concepts": [ "Multiplying Binomials", "Product of Powers", "Square of a Binomial" ] } ## Write the expression as a product of two binomials $$ (3a^4 + 4)^2 = (3a^4 + 4)(3a^4 + 4) $$ ## Expand the product using the FOIL method $$ (3a^4)(3a^4) + (3a^4)(4) + (4)(3a^4) + (4)(4) $$ ## Simplify each term and combine like terms $$ 9a^8 + 12a^4 + 12a^4 + 16 = 9a^8 + 24a^4 + 16 $$

(A) $6a^4 + 8$

(B) $9a^8 + 16$

(C) $9a^8 + 24a^4 + 16$

(D) $9a^{16} + 24a^4 + 16$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Multiplying Binomials" ] }

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QUESTION IMAGE

Question

Explanation:

Write the expression as a product of two binomials

Expand the product using the FOIL method

Simplify each term and combine like terms

Answer: