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3 years ago

Quickly compute the following differences of squares. (a). 64^2 − 14^2 (b). 112^2 − 88^2 (c). 785^2 − 215^2

Mathematics

1 answer:

VikaD [51]3 years ago

5 0

Answer:

(a) 3900

(b) 4800

Step-by-step explanation:

We have given

(a) $64^2-14^2$

We know the algebraic equation $a^2-b^2=(a+b)(a-b)$

So $64^2-14^2=(64+14)(64-14)=3900$

(b) We know the algebraic equation $a^2-b^2=(a+b)(a-b)$

$112^-88^2=(112+88)(112-88)=4800$

$785^2-215^2=(785+215)(785-215)=570000$

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Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?

Lostsunrise [7]

Answer:

The correct options, rearranged, are:

Options:

$A)(a^2+ab+b^2)/(a-b)\\\\B)(a^2-ab+b^2)/(a+b)\\\\C)(a^3+0a^2+0ab^2-b^3)/(a+b))\\\\ D)(a^3+0a^2+0ab^2-b^3)/(a-b)$

And the asnwer is the last option (D).

Explanation:

You need to find which long division can be used to prove the formula for factoring the difference of two perfect cubes.

The difference of two perfect cubes may be represented by:

$a^3-b^3$

And it is, as a very well known special case:

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Then, to prove, it you must divide the left side, $a^3-b^3$ , by the first factor of the right side, $a-b$

Note that, to preserve the places of each term, you can write:

$(a^3-b^3)=(a^3+0a^2+0ab^2-b^3)$

Then, you have:

$(a^3+0a^2+0ab^2-b^3)=(a-b)(a^2+ab+b^2)$

By the division property of equality, you can divide both sides by the same factor, which in this case will be the binomial, and you get:

$(a^3+0a^2+0ab^2-b^3)/(a-b)=(a^2+ab+b^2)$

That is the last option (D).

3 0

3 years ago

Read 2 more answers

Triangle JKL is formed by plotting three points, as shown below. What is the length of side<br> JK?

AURORKA [14]

Answer:

Step-by-step explanation:

You have to add the boxes between j and k and that’s how u get your length

8 0

3 years ago

Mr. Fink's economy car can travel 420 miles on a 12-gallon tank of gas. Determine how many miles he can travel on 8 gallons.

Sphinxa [80]

Answer:

280 miles

Step-by-step explanation:

So, 420 miles=12 gallons

That means that for 1 gallon you would be able to go 35 miles.

Just multiply that by 8. 35*8=280

3 0

3 years ago

What is the counterexample for the city of Portland is in Oregon

Dmitry_Shevchenko [17]

A counter example disproves a statement.

The counter example for : the city of Portland is in Oregon would be : the city of Portland is in Maine.

The city named Portland can be found in both states.

7 0

3 years ago

If M is the midpoint of line segment XY, find the coordinates of X if M(-3,1) and Y(-8,4)

lozanna [386]

Answer:

The coordinates of point X are (-11/2, 5/2)

Step-by-step explanation:

To find the coordinates of X , we shall apply the midpoint formula;

Mathematically, that would be;

(x , y) = (x1 + x2)/2 , (y1 + y2)/2

From the question

x1 = -3 , x2 = -8

y1 = 1 , y2 = 4

So substituting these values, we have;

(x ,y) = (-3-8)/2, (1 + 4)/2

(x ,y) = -11/2, 5/2

6 0

4 years ago