Question

Please help me i don't know what to do please show your work

Answer 1

20) 6c-6

22)i think before simplifying is:

-8(2)+5-2(2)-4+5(2) then. you simplify

16+5-4-4+10 =21

23) Yes, because when you solve for both equations they both give you 11x exponent of 2 +3y

25) 3(3+x)

Answer 2

Distributive Property

The distributive property lets you group or ungroup terms using parentheses. It lets you multiply an external factor by every term in parentheses, expressing the result as a sum:

... a(b + c) = ab + ac . . . . . . factor a multiplies the terms b and c

and it lets you remove a common factor from different terms, putting that factor outside parentheses:

... ab + ac = a(b + c)

The letters a, b, c here can stand for any number or expression.

Homework

20. To do this problem, you need to eliminate the parentheses using the distributive property. Then, "collect terms," which is another application of the distributive property. The external factor outside the parentheses is (-2/3). Multiply that by each term in parentheses, and add the results.

After that, recognize that c is a factor of two of the terms. Add their coefficients to simplify that sum to one term.

$-\dfrac{2}{3}(12c-9)+14c=\left(-\dfrac{2}{3}\right)(12c)+\left(-\dfrac{2}{3}\right)(-9)+14c=-8c+6+14c\\\\=c(-8+14)+6\\\\=6c+6$

22. You are to evaluate the expression with x=2 two ways: as is, and after you simplify it by combining like terms.

As is:

$-8x+5-2x-4+5x\\=-8(2)+5-2(2)-4+5(2)\\=-16+5-4-4+10\\=-9$

Simplified:

$-8x+5-2x-4+5x\\=x(-8-2+5)+(5-4)=-5x+1\\=-5(2)+1=-10+1\\=-9$

I prefer simplifying the expression first. The number of calculations and chances for error are reduced.

23. It is convenient to check for equivalence after simplifying both expressions.

First Expression:

$8x^2+3\left(x^2+y\right)=8x^2+3x^2+3y=11x^2+3y$

Second Expression:

$7x^2+7y +4x^2-4y=(7+4)x^2+(7-4)y=11x^2+3y$

The simplified forms of the expressions are identical, so we conclude the expressions are equivalent.

25. The area of a rectangle is the product of its length and width. Here, you are asked to simplify the product of (3+x) ft and 3 ft.

$((3+x)\,\text{ft})(3\,\text{ft})=(3\,\text{ft})\cdot (3\,\text{ft})+(x\,\text{ft})\cdot (3\,\text{ft})=9\,\text{ft}^2+3x\,\text{ft}^2\\\\=(3x+9)\,\text{ft}^2$

In the last form of this expression, we have used "standard form" which has the degree of the variable decreasing in terms left to right. The units are factored out to make the expression a bit less cumbersome.