Question

what is the product?$(x^{4})(3x^{3}-2)(4x^{2}+5x)?LXB012x^{24}+15x^{12}-8x^{8}-10x^{4}LXB112x^{24}-10x^{4}$

Explanation:

Step1: Multiply the two binomials

Use the distributive property (FOIL method):
$$(3x^3 - 2)(4x^2 + 5x) = 3x^3 \cdot 4x^2 + 3x^3 \cdot 5x - 2 \cdot 4x^2 - 2 \cdot 5x$$
$$= 12x^{5} + 15x^{4} - 8x^2 - 10x$$

Step2: Multiply by $x^4$

Distribute $x^4$ to each term:
$$x^4(12x^{5} + 15x^{4} - 8x^2 - 10x) = x^4 \cdot 12x^5 + x^4 \cdot 15x^4 - x^4 \cdot 8x^2 - x^4 \cdot 10x$$
$$= 12x^{9} + 15x^{8} - 8x^6 - 10x^5$$

Answer:

A. $12x^9 + 15x^8 - 8x^6 - 10x^5$