Question

I need help simplifying both of these. thank you!

Answer 1

1. -100x +100; 3
2. 5x +81; 162

Explanation:

The distributive property is your friend. It tells you ...

a(b + c) = ab + ac

It can also be used to simplify the product of binomials (or other polynomials).

(a +b)^2 = (a +b)(a +b) = a(a +b) + b(a +b) = a^2 +ab +ab +b^2

(a +b)^2 = a^2 +2ab + b^2 . . . . . . . worth remembering

1. (x -10)^2 -x(x +80) = (x^2 -20x +100) +(-x^2 -80x)

= -100x +100 . . . . . . simplified form

For the purposes of calculation, it can be easier to factor out 100:

= 100 (1 -x)

Then for x = 0.97

= 100(1 -0.97) = 100(0.03) = 3

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2. (2x +9)^2 -x(4x +31) = (4x^2 +36x +81) -4x^2 -31x = 5x +81

For x = 16.2, this is ...

5(16.2) +81 = 81 +81 = 162

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The purpose of the attachment is to show the evaluation is correct.