SOLUTION: I need some help with practice questions, About monomials, polynomials, and factoring, simplifying. [Simplifying polynomials] (5x+4)(5x-4) 2x(x+5)+x(3-x) 5ab^2b(7ab^2+3a

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need some help with practice questions, About monomials, polynomials, and factoring, simplifying. [Simplifying polynomials] (5x+4)(5x-4) 2x(x+5)+x(3-x) 5ab^2b(7ab^2+3a      Log On


   

Question 540641: I need some help with practice questions,
About monomials, polynomials, and factoring, simplifying.
[Simplifying polynomials]
(5x+4)(5x-4)
2x(x+5)+x(3-x)
5ab^2b(7ab^2+3a-4b)
(5m^2-2mp-6p^2)-2(-3m^2+5mp-p^2) (THIS ONE IS REALLY HARD)
&This is the only simplifying expression question I have trouble on:
(3x^2y^6)(-4x^2y^6)
If you could help, step by step.
thank you!
Found 2 solutions by mananth, KMST:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
(5x+4)(5x-4)
Multiply each term of first to the second
5x(5x-4)+4(5x-4)
25x%5E2-20x%2B20x-16
25x%5E2-16
----
2x(x+5)+x(3-x)
2x%5E2%2B10x%2B3x-x%5E2
x%5E2%2B13x
-----
5a%2Ab%5E2%2Ab%287ab%5E2%2B3a-4b%29
35a%5E2b%5E5%2B15a%5E2b%5E3-20ab%5E4
------------
%285m%5E2-2mp-6p%5E2%29-2%28-3m%5E2%2B5mp-p%5E2%29+
5m%5E2-2mp-6p%5E2%2B6m%5E2-10mp%2B2p%5E2
11m%5E2-12mp-4p%5E2

&This is the only simplifying expression question I have trouble on:
%283x%5E2y%5E6%29%28-4x%5E2y%5E6%29
-12x%5E4%2Ay%5E12
m.ananth@hotmail.ca

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
%285x%2B4%29%285x-4%29 is a sum of two terms/numbers times their difference, and that equals the difference of the squares. They teach you that as a special product, usually with the formula %28a%2Bb%29%28a-b%29=a%5E2-b%5E2
%285x%2B4%29%285x-4%29=%285x%29%5E2-4%5E2=5%5E2%2Ax%5E2-16=25x%5E2-16
If you were not taught about special products, you may have to multiply and simplify, maybe like this

You can amaze people with feats of mental math using difference of squares. How much is 801 times 799? Well, that's
801%2A799=%28800%2B1%29%28800-1%29=800%5E2-1%5E2=640000-1=639999
How much is 25 times 35? 25%2A35=%2830-5%29%2830%2B5%29=30%5E2-5%5E2=900-25=875



The first step was multiplying that -2 times the second parenthesis applying the distributive property. I really see that -2 as +(-2), but I do not always write it out the way I see it. I only do it when I want to avoid confusing myself. Later on, you'll notice that I changed -2mp to +(-2mp). I did that to avoid confusing myself. I believe algebra would be easier if everyone realized that subtraction does not really exist, and 7-3 is really 7+(-3). If you take the sign as part of the number, you get less confused. When you see a minus sign in front of a parenthesis, as in -%28x-3y%29 take it to mean there is a +(-1) instead of the minus sign to state +(-1)(x-3y).