Question

How do you multiply `(x ^ { 2} + 8x + 1) ( 7x + 4)`?

Answer 1

See the entire solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(x^2) + color(red)(8x) + color(red)(1))(color(blue)(7x) + color(blue)(4))` becomes:

`(color(red)(x^2) xx color(blue)(7x)) + (color(red)(x^2) xx color(blue)(4)) + (color(red)(8x) xx color(blue)(7x)) + (color(red)(8x) xx color(blue)(4)) + (color(red)(1) xx color(blue)(7x)) + (color(red)(1) xx color(blue)(4))`

`7x^3 + 4x^2 + 56x^2 + 32x + 7x + 4`

We can now combine like terms:

`7x^3 + (4 + 56)x^2 + (32 + 7)x + 4`

`7x^3 + 60x^2 + 39x + 4`

Answer 2

When you're multiplying a polynomial with a binomial, you need to distribute each part of the binomial.

Explanation:

`7x` would be distributed and multiplied with `x^2`, `8x`, and `1`. This would make the items inside the parentheses `(7x^3 + 56x^2 +7x)`. Then, take this equation and multiply it by four , the remaining number. This leaves you with an answer of `28x^3 + 224x^2 + 28x`. You can simplify this to `x^3 + 8x^2 + 28x` by dividing by a common denominator of 28.