Question

How do you multiply `5x ^ { 2} ( 5x ^ { 2} + 7x + 3)`?

Answer 1

`5x^2(5x^2+7x+3)=color(red)(25x^4+35x^3+15x)`

Explanation:

By the distributive property:
`color(white)("XXX")color(blue)a(color(green)b+color(orange)c+color(magenta)d) = color(blue)acolor(green)b+color(blue)acolor(orange)c+color(blue)acolor(magenta)d`
So
`color(white)("XXX")color(red)(5x^2)(color(blue)(5x^2)+color(orange)(7x)+color(magenta)3) =color(blue)(5x^2) * color(green)(5x^2)+color(blue)(5x^2) * color(orange)(7x)+color(blue)(5x^2) * color(magenta)3`

`color(white)("XXXXXXXXXXXXXX")=25x^2 color(white)("xxx")+35x^3color(white)("xxx")+15x^2`