# Simplifying using algebraic operations

I came across this question while doing homework out of the Philips Exeter Academy Mathematics 1 textbook, and do not usderstand what to do.

Here is the question: "In each of the following, use appropriate algebraic operations to remove the parentheses and combine like terms. Leave your answers in simple form.

(a) x(2x)+2(x+5) (b) 2x(5x-2)+3(6x+7) (c) 5m(3m-2n)+4n(3m-2n) "

I'm having ahard time understanding what the question means getting rid of the parentheses by using "algebraic operations", and I tried doing the multiplication, but I couldn't get rid of the parentheses successfully.

Could someone please walk me through and help me understand this problem? Thanks

• my tag is probably wrong – john knox Oct 22 '17 at 17:24
• (a): $2x^2+2x+10$. – Mauro ALLEGRANZA Oct 22 '17 at 17:26

HINTS

$x(2x)=x*(2*x)=x*2*x=2*x*x=2x^2$

Does this make sense? Can you see why it holds?

Now for combining like terms:

$2x^2+2x+3y^3-6y=2x(x+1)+3y(y^2-2)$

where we have the $"x"$s and $"y"$s neatly packaged in two instead of four terms.

This is just an example of applying the basic properties: Commutative, Associative and Distributive.

(b) \begin{align*} 2x(5x-2)+3(6x+7)&=2x\times 5x-2x\times 2+3\times6x +3\times 7\\ &=10x^2-4x+18x+21\\ &=10x^2+14x+21 \end{align*}