Answer: 2x^2-6x-8
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Step-by-step explanation:
Let y = x+1
This means (x+1)(2x-8) is the same as y(2x-8)
Distribute the y term through to get:
y(2x-8) = 2xy - 8y
Then plug y = x+1 back in and distribute twice more like so
2xy - 8y
2x( y ) - 8( y )
2x(x+1) - 8(x+1)
2x^2+2x - 8x-8
2x^2-6x-8
Therefore, (x+1)(2x-8) = 2x^2-6x-8
It is a trinomial because the result has three terms.
It's also a quadratic because the largest exponent is 2.
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Another approach is to use the FOIL rule
F: first
O: outer
I: inner
L: last
The first terms of (x+1) and (2x-8) are x and 2x respectively, so x*2x = 2x^2 is the product of them.
The outer terms are x and -8, which multiply to -8x
The inner terms are 1 and 2x which multiply to 2x
The last pair of terms are 1 and -8 which multiply to -8
We then get 2x^2-8x+2x-8 which turns into 2x^2-6x-8
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Another approach:
Perhaps my favorite approach is to use the box method. This is a grid like visual method to keep track of all the terms. See below.
We list the terms of x+1 along the left, and the terms of 2x-8 along the top. To fill out the inner boxes, we multiply the outside terms
For instance, x times 2x gets us 2x^2 in the upper left corner.
We have four boxes, so we'll have four products. Those terms being the terms from 2x^2-8x+2x-8 mentioned in the previous section. That combines to 2x^2-6x-8