can someone help me with my math hw?

Question

Factor completely:
1.) 2asquare + 2a - 84
2.) 6axsquare - 24aysquare

Explain and thankyou

Answer 1

Question 1
2a² + 2a - 84
2(a² + a - 42)
2(a + 7)(a - 6)

Question 2
(6a)(x² - 4y²)
(6a) (x - 2y)(x + 2y)

Answer 2

1) Factors of the the first and last coefficients:

2: 1, 2
84: 1, 2, 3, 4, 6, 7, 12, 14, 16, 21, 28, 42, 84

Now you have to think of a combination of a factor pair of 2 and 84 which will give you the middle coefficient of 2 when added or subtracted from each other:

I would start with 7 and 12 from 84 (they are the middle factors).

2*7 = 14
1*12 = 12
14-12 = 2

Perfect

We know the 12 should be negative and the 7 should be positive since we should get 14-12 in the end:

(2a-12)(a+7)

Notice the 2a will multiply by the 7 and get 14a
Then the -12 will get multiplied with a to get -12a
14a-12a = 2a

That is all that matters in these problems.

Pull out the 2 in the first term and we are done:

2(a-6)(a+7)

2) 6ax^2 - 24ay^2

Okay, this one you need to pull the common factor from both terms.

The common factor here is 6a, pulling this out yields:

6a(x^2 - 4y^2)

But, you are not done!

You now have the difference of two squares.

The square root of x^2 is x
The square root of 4y^2 is 2y

So we now get:

6x(x+2y)(x-2y)

Look in your text book for the difference of two squares for more examples of why I did this.

Answer 3

2a^2 + 2a - 84
the common thing we can pull from this is 2, because all the terms in the expression are divisible by 2
we get
a^2 + a - 42
now we have to find two factors of 42 that have a difference of 1 so that we can get a if we needed to get 2a, we would find the factors of 42 that have a difference of 2
in this case, the numbers are 6 and 7
then we substitute the numbers

2(a+7)(a-6)
we don't write 7 and 6 alternatively because 7-6 = 1 which we need to get because a = 1a. 6 - 7 = -1, and then we would get -a/

u want to do the same thing for the other problem and u should get
6ax^2 - 24ay^2
6a(x^2 - 4y^2)
Nvr mind, this is a perfect square
to find perfect squares, (this only works if the expression is something - something.) you basically take the square root of the first number and the square root of the second number and then we put them into this equation.

(sqroot of term #1+sqroot of term#2) * (sqroot of term #1-sqroot of term#2)
notice that the difference between the terms in the brackets are that in the second bracket the terms are subtracted

u should get 6a(x + 2y)(x - 2y)

hope i helped srry this is soo long

Answer 4

1. 2a^2 +2a - 84 = 0
a^2 + a - 42 = 0 lowest term
(a+7)(a-6) = 0 find factors of 42 that have the sum of 1
a = {-7, 6} set a+7=0 and a-6=0 and transpose

2. 6ax^2 - 24ay^2 = 0
ax^2 - 4ay^2 = 0 lowest term
a(x^2 - 4y^2) = 0 factor a
a(x-2y)(x+2y) = 0 sum and difference of 2 terms

Answer 5

1)
2a² + 2a - 84 = 0

Factor out a 2 for simplicity:

a² + a - 42 = 0

What two numbers multiply to -42, and add to 1?

-6 and 7

(a + 7)(a - 6) = 0

a = -7 or a = 6

2)
6ax² - 24ay² = 0
Factor out 6a

6a(x² - 4y²) = 0

Now factor inside using difference of squares:

6a(x + 2y)(x - 2y) = 0

a = 0
or
x = -2y
or
x = 2y

Answer 6

1) Problem: 2a^2 + 2a - 84

Solution:

Factor out the 2....

2(a^2 + a - 42)

Finding two #s when multiplied will equal to -42, those same #s must also add up to 1....

7*-6 = -42
7+ - 6 = 7-6 = 1

Thus:

2(a + 7)(a - 6) = Answer

2) Problem: 6ax^2 - 24ay^2

Factor out 6....

6a(x^2 - 4y^2)

Similar to the first, x*x = x^2 and 2y*2y = 4y^2, factoring....

6a(x - 2y)(x+2y) b/c of the - sign between x and y....

Thus: 6a(x-2y)(x+2y) = Answer....

Answer 7

2a^2 + 2a - 84
2(a^2 + a - 42)

6ax^2 - 24ay^2
6(ax^2 - 4ay^2)
6(a)(x^2 - 4y^2)
2 * 3 * a * (x + 2y) * (x - 2y)

The prime factors are:
2, 3, a, x + 2y and x - 2y

Answer 8

2a^2 + 2a - 84
= 2(a^2 + a - 42)
= 2(a+7)(a-6)

6ax^2- 24ay^2
= 6a(x^2-4y^2)
= 6a(x+2y)(x-2y)

Answer 9

2a^2+2a-84
=2(a^2+a-42)
=2(a+7)(a-6)

6ax^2-24ay^2
=6a(x^2-4y^2)
=6a(x+2y)(x-2y)