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(6x2 - 4x + 11)(5x - 8) please simplify this

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3 Answers

First multiply each term in the first parenthesis by only the first term in the second parenthesis.

6x2 * 5x = 30x3

-4x * 5x = -20x2

11 * 5x  = 55x

Next multiply each term in the first parenthesis by only the second term in the second parenthesis.

6x2 * -8 = -48x2

-4x * -8 = 32x

11 * -8 = -88

Now add all of your like terms or the terms that have the same degrees.

 x3s              x2s       xs          coefficients (or no x just a number)

30x3           -20x2     55x

              + -48x2  + 32x            -88

30x3              -68x2    87x            -88

So, your answer is:

30x3 - 68x2 + 87x - 88

Multiply out all the terms as such:

5x(6x2 - 4x +11) - 8(6x2 - 4x + 11)

30x3 - 20x2 + 55x - 48x2 + 32x -  88

Collect similar terms:

30x3 - 68x2 + 87x + 88  ยป   Answer 

What you have to do in such a case, is to muliply each term of each factor by each term of other factors. As ax+bx = (a+b)x, (a+b)(x+y) = (a+b)x+(a+b)y = ax+bx+ay+by, so (a+b)(x+y) = ax+ay+bx+by.

Here, one way is to first distribute 5x and -8, which means that

(6x2-4x+11)(5x-8) = 5x(6x2-4x+11)-8(6x2-4x+11), then multiply 5x by 6x2, by -4x and by 11, and multiply -8 by each term too. You'll have 5x(6x2-4x+11)-8(6x2-4x+11) = 30x3-20x2+55x-48x2+32x-88.

Finally, add the coefficients of each degree of x to have 30x3-68x2+87x-88

(6x2-4x+11)(5x-8) = 30x3-68x2+87x-88