Given:
Consider the given function:
To prove:
Solution:
We have,
Substituting 
, we get
Substituting 
, we get
Substituting 
, we get
Using the algebraic formula, we get
![[\because b^2-a^2=(b-a)(b+a)]](https://tex.z-dn.net/?f=%5B%5Cbecause%20b%5E2-a%5E2%3D%28b-a%29%28b%2Ba%29%5D)
[Commutative property of addition]
Now,
Hence proved.
For example,area = a, length = l, width = w
First we write two equations. The easier equation is the area equation, which we know to be
a = l x w
So that the first equation is :
<span>96 = l x w </span>
we make the second equation of the following statements :
<em>The length of a rectangle is 2 foot less than 3 times its width.</em>
<span>so it becomes :
l = 3w - 2
</span>
<span>To solve, we can use the substitution method.
</span>
![96 = l \times w\\96=(3w-2) \times w\\96=3w^{2}-2w\\3w^{2}-2w-96=0~~~~~~[now\ factor\ the\ equation]\\ (3w+16)(w-6)=0](https://tex.z-dn.net/?f=96%20%3D%20l%20%5Ctimes%20w%5C%5C96%3D%283w-2%29%20%5Ctimes%20w%5C%5C96%3D3w%5E%7B2%7D-2w%5C%5C3w%5E%7B2%7D-2w-96%3D0~~~~~~%5Bnow%5C%20factor%5C%20the%5C%20equation%5D%5C%5C%20%283w%2B16%29%28w-6%29%3D0)
<span><em>So if our width is 6, Now substitute the value of w = 6 into equation 2 </em></span>
So "w" = 6 and "l" = 16, and if we multiply them together, we get the correct area, 96. So our dimensions are 6 by 16.
The llike terms are {17xy^2, -13xy^2} {9, 3} {8y^3, -6y^3} {10x, -9x} first combine 9 and 3 now your new equation is 12 <span>+ 17xy^2 + 8y^3 + 10x –13xy^2 – 9x – 6y^3 then add 17xy^2 and -13xy^2 your new equation is 12 + 4xy^2 </span><span>+ 8y^3 + 10x – 9x – 6y^3 now combine 8y^3 and 6y^3 your new equation is 12 + 4xy^2 + 2y^3 </span><span>+ 10x – 9x now combine 10 and -9x and your answer is </span><span><span>12 + 4xy^2 + 2y^3 <span>+ x</span></span> </span>
4. 28.5 squared centimeter
5. height=18 ft
7. The triangle will be bigger. Since this scale factor is 4, then that means that the 2-D plane will be bigger.
8. The perimeter will get bigger.
