Question

Multiply the polynomials. Simplify the answer. Show your work. (5x^2+8x-6)(8x^2+3x+1)

Answer 1

Use the distributive property and $a^n\cdot a^m=a^{n+m}$

$(5x^2+8x-6)(8x^2+3x+1)\\\\=(5x^2)(8x^2)+(5x^2)(3x)+(5x^2)(1)+(8x)(8x^2)+(8x)(3x)+(8x)(1)+(-6)(8x^2)+(-6)(3x)+(-6)(1)\\\\=40x^4+15x^3+5x^2+64x^3+24x^2+8x-48x^2-18x-6\\\\=40x^4+(15x^3+64x^3)+(5x^2+24x^2-48x^2)+(8x-18x)-6\\\\=40x^4+79x^3-19x^2-10x-6$

Answer 2

40x^4 + 79x^3 - 19x^2 - 10x - 6

5x^2 + 8x - 6(8x^2 + 3x + 1)

Distributive property.

40x^4 + 15x^3 + 5x^2 + 64x^3 + 24x^2 + 8x - 48x^2 - 18x - 6

Combine like terms.

40x^4 + 79x^3 - 19x^2 - 10x - 6