anonymous one year ago what is the simplest form of this expression 4(-5y+4)+(-7)(-3y+1)

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1. Owlcoffee

Apply the distributive property and operate similar terms, that'd give you the answer.

2. anonymous

need more help then that

3. anonymous

@Nnesha

4. anonymous

@welshfella

5. Nnesha

distribute parentheses by outside terms (as owl suggested )

6. Nnesha

here is an example $\huge\rm \color{red}{a}(b+c)=\color{red}{a} \times b + \color{red}{a} \times c =\color{reD}{a}b+\color{reD}{a}c$

7. Nnesha

|dw:1438981491633:dw|

8. Owlcoffee

Just to extend Nneshas suggestion: $(4)(-5y)+(4)(4)+(-7)(-3y)+(-7)(1)$

9. anonymous

-20y+16+21y+-7 ?

10. Owlcoffee

Good, now, operate the terms that do and do not have "y" on their right side.

11. anonymous

what do you mean

12. Owlcoffee

It will look like this: $(-20+21)y +(16-7)$

13. anonymous

okay and can you just show me how to solve this step by step like in one of those pics things so i can fully understand this

14. anonymous

?

15. Owlcoffee

Starting out with: $4(-5y+4)+(-7)(-3y+1)$ Whenever you want to simplify any mathematical expression you first get rid of what is called "groupings", which in this case is the parenthesis, so in order to do that, you always apply Distributive property: $$a(b+c)=ab+ac$$ So, applying distributive property on the first and second parenthesis with their corresponding "outside term": $-20y+16+21y-7$ This is a much simpler way of viewing the first mathematical expression but not the simplest, so in order to simplify it more, we will get rid of operations, those being addition and sustraction as you can see. The only way to do that is to reduce the terms of the mathematical expression, you might as well know that a "term" in mathematics is any number, variable or both, separated by a basic operation, that being "+" or "-". And we can reduce terms if we can see that the only variable present is "y" and there are more than one term with a "y" on them, so we will take "common factor" (Which is the reverse of distributive) "y" on the terms that has it: $(-20+21)y+16-7$ That is also called "grouping like terms". now it's just a matter of arithmetics, which I will suppose you already know: $(1)y+9$ Or better written as: $y+9$

16. anonymous

thank you