(4x3 + 5)(2x3 + 3) = 8x6 + Tx3 + 15

2 min read Jun 16, 2024

Solving for the Unknown Coefficient 't'

This article will guide you through the process of finding the value of the unknown coefficient 't' in the equation:

(4x³ + 5)(2x³ + 3) = 8x⁶ + tx³ + 15

The first step is to expand the left-hand side of the equation using the distributive property (also known as FOIL - First, Outer, Inner, Last):

(4x³ + 5)(2x³ + 3) = (4x³ * 2x³) + (4x³ * 3) + (5 * 2x³) + (5 * 3)

Simplifying the terms:

(4x³ + 5)(2x³ + 3) = 8x⁶ + 12x³ + 10x³ + 15

Combining like terms:

(4x³ + 5)(2x³ + 3) = 8x⁶ + 22x³ + 15

Now we can compare the expanded left-hand side with the right-hand side of the original equation:

8x⁶ + 22x³ + 15 = 8x⁶ + tx³ + 15

We can see that the coefficients of the x⁶ and constant terms match. The only difference is in the coefficient of the x³ term.

Therefore, we can conclude:

t = 22

We have successfully solved for the unknown coefficient 't' in the equation:

(4x³ + 5)(2x³ + 3) = 8x⁶ + tx³ + 15

The value of 't' is 22.