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Otrada [13]
3 years ago
12

Factor the algebraic expression

Mathematics
2 answers:
Reika [66]3 years ago
7 0

Step-by-step explanation:

look at the attachment......

Mila [183]3 years ago
4 0

Answer:

<h2> [x - y]×[x + y - 2] </h2>

Step-by-step explanation:

(x - 1)² - (y - 1)² has the form of a² - b² which is equal to (a - b)(a + b) where a = x-1 and b = y - 1

then

(x - 1)² - (y - 1)² = [(x - 1) - (y - 1)]×[(x - 1) + (y - 1)]

                      = [x - y]×[x + y - 2]

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Step-by-step explanation:

We are given the following:

\frac{x}{5}=q_1+\frac{4}{5}      (equ. 1)

\frac{y}{5}=q_2+\frac{1}{5}      (equ. 2)

We are asked:

\frac{x+y}{5}=q_3+\frac{r}{5}  (equ. 3) , what is r?

The q_i's represent the quotients you get.

r is the remainder of dividing x+y by 5.

We know that r is a number in {0,1,2,3,4}.

x=5q_1+4 (I got this by multiplying both sides of equ 1. by 5.)

y=5q_2+1 (I got this by multiplying both sides of equ 2. by 5.)

Let's add these equations together:

x+y=(5q_1+5q_2)+(4+1)

Factoring the 5 out for the q_i's part and simplify 4+1 gives:

x+y=5(q_1+q_2)+5

So 5 can't be the remainder of dividing something by 5 but see that we can factor this right hand expression more as:

x+y=5(q_1+q_2+1)

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Let's do an example if you are not convinced at this point that the remainder will be 0.

So choose x=9 since 9/5 gives a remainder of 4.

And choose y=16 since 16/5 gives a remainder of 1.

x+y=9+16=25 and 25/5 gives a remainder of 0.

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