Question

select the correct answer
which expression is equivalent to this polynomial expression?
$(2x^5 + 3y^4)(-4x^2 + 9y^4)$
\\(\circ\\) a. $-8x^7 + 27y^8$
\\(\circ\\) b. $-2x^{10} + 11x^5y^4 - x^2y^4 + 12y^{16}$
\\(\circ\\) c. $-2x^7 + 11x^5y^4 - x^2y^4 + 12y^8$
\\(\circ\\) d. $-8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8$

Explanation:

Step1: Apply Distributive Property (FOIL)

Multiply each term in the first polynomial by each term in the second polynomial:

$$
LATEXBLOCK0
$$

Step2: Simplify Each Term

• For \((2x^5)(-4x^2)\): Use the rule \(a^m \cdot a^n = a^{m + n}\) and multiply coefficients: \(2\times(-4)x^{5 + 2}=-8x^7\)
• For \((2x^5)(9y^4)\): Multiply coefficients: \(2\times9x^5y^4 = 18x^5y^4\)
• For \((3y^4)(-4x^2)\): Multiply coefficients: \(3\times(-4)x^2y^4=-12x^2y^4\)
• For \((3y^4)(9y^4)\): Use the rule \(a^m \cdot a^n = a^{m + n}\) and multiply coefficients: \(3\times9y^{4 + 4}=27y^8\)

Step3: Combine Simplified Terms

$$ -8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8 $$

Answer:

D. \(-8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8\)