need help

[sturdy wasp]

i need some help with this one

(x-4)(x²+x-2)
The Answer is x³-3x²-6x+8

i know most of it except how to find -3x² i thinked about it and kinda found a way but im not sure can anyone help me with it

[north vault]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations

[cunning epoch]

x(x) = x²
-4(x²)=-4x²
The sum of the two like terms above is -3x².

[hidden cedar]

how are you calculating this?

the most straightfoward way is probably to break it up as

x (x²+x-2) - 4 (x²+x-2)

[bright briar]

First Solution
Above this message ^^

Second Solution
$({\color{yellow}x}-4)({\color{yellow}x^2}+x-2) = x^3\ ({\color{yellow}x}-4)(x^2+{\color{yellow}x}-2) = x^2\({\color{yellow}x}-4)(x^2+x{\color{yellow}-2}) = -2x\(x{\color{yellow}-4})({\color{yellow}x^2}+x-2) = -4x^2\$

[signal tree]

itsme2800

[bright briar]

$(x{\color{yellow}-4})(x^2{\color{yellow}+x}-2) = -4x\(x{\color{yellow}-4})(x^2+x{\color{yellow}-2}) = 8$

Therefore,
$x^3 + x^2 - 2x-4x^2-4x+8 = {\color{green}x^3 -3x^2-6x+8}$

[signal tree]

itsme2800

[hoary kayak]

You can distribute:

(x-4)(x²+x-2)=x(x²+x-2) - 4(x²+x-2)

x^3 + x^2 - 2x - 4x^2 - 4x + 8