Question

what value of \\(t\\) makes the statement true?
\\((4x^3 + 5)(2x^3 + 3) = 8x^6 + tx^3 + 15\\)

\\(t = \\)

Explanation:

Expand the left side of the equation

$$ (4x^3 + 5)(2x^3 + 3) = (4x^3)(2x^3) + (4x^3)(3) + (5)(2x^3) + (5)(3) $$

Simplify the terms

$$ 8x^6 + 12x^3 + 10x^3 + 15 = 8x^6 + 22x^3 + 15 $$

Compare coefficients to solve for t

$$ 8x^6 + 22x^3 + 15 = 8x^6 + tx^3 + 15 \implies t = 22 $$

Answer:

What value of \(t\) makes the statement true?

$$(4x^3 + 5)(2x^3 + 3) = 8x^6 + tx^3 + 15$$

\(t =\) <blank>22</blank>