Question

Multiply the polynomials.

Answer 1

$48x^3-4x^2+18x-40 \text{ is the product of } (8x^2+6x+8)(6x-5)$

Solution:

Given that we have to multiply the polynomials

$(8x^2+6x+8)(6x-5)$

Multiplying polynomials is similar to multiplying numbers

When you multiply two terms together you must multiply the coefficient (numbers) and add the exponents

Let us multiply the given polynomials

$\rightarrow (8x^2+6x+8)(6x-5)$

Multiply each term in first bracket with each term in second bracket

$\rightarrow (8x^2)(6x) -5(8x^2)+6x(6x)+6x(-5)+8(6x)+8(-5)$

Add the exponents and multiply the coefficients

$\rightarrow 48x^3-40x^2+36x^2-30x+48x-40$

Combine the like terms -30x and 48x

$\rightarrow 48x^3-40x^2+36x^2+18x-40$

Combine the like terms $-40x^2 \text{ and } 36x^2$

$\rightarrow 48x^3-4x^2+18x-40$

Thus the polynomials has been multiplied