Question

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

Explanation:

Step1: Expand left-hand side

Use FOIL method:
$$(4x^3 + 5)(2x^3 + 3) = 4x^3 \cdot 2x^3 + 4x^3 \cdot 3 + 5 \cdot 2x^3 + 5 \cdot 3$$

Step2: Calculate each term

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

Step3: Combine like terms

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

Step4: Match coefficients of $x^3$

Set equal to right-hand side $8x^6 + tx^3 + 15$

Answer:

$22$