Y = ___x - ___<br><br> Enter the missing numbers separated by a comma and no spaces!

(i) Write the expansion of (x + y)² and (x - y)². (ii) Find (x + y)² - (x - y)² (iii) Write 12 as the difference of two perfect

zaharov [31]

Answer:

1a (x + y)² = x² + 2xy + y²

1b. (x - y)² = x² - 2xy + y²

2. (x + y)² - (x - y)² = 4xy

3. 4² – 2² = 12

Step-by-step explanation:

1a. Expansion of (x + y)²

(x + y)² = (x + y)(x + y)

(x + y)² = x(x + y) + y(x + y)

(x + y)² = x² + xy + xy + y²

(x + y)² = x² + 2xy + y²

1b. Expansion of (x - y)²

(x - y)² = (x - y)(x - y)

(x - y)² = x(x - y) - y(x - y)

(x - y)² = x² - xy - xy + y²

(x - y)² = x² - 2xy + y²

2. Determination of (x + y)² - (x - y)²

This can be obtained as follow

(x + y)² = x² + 2xy + y²

(x - y)² = x² - 2xy + y²

(x + y)² - (x - y)² = x² + 2xy + y² - (x² - 2xy + y²)

= x² + 2xy + y² - x² + 2xy - y²

= x² - x² + 2xy + 2xy + y² - y²

= 2xy + 2xy

= 4xy

(x + y)² - (x - y)² = 4xy

3. Writing 12 as the difference of two perfect square.

To do this, we shall subtract 12 from a perfect square to obtain a number which has a perfect square root.

We'll begin by 4

4² – 12

16 – 12 = 4

Find the square root of 4

√4 = 2

4 has a square root of 2.

Thus,

4² – 12 = 4

4² – 12 = 2²

Rearrange

4² – 2² = 12

Therefore, 12 as a difference of two perfect square is 4² – 2²

7 0

3 years ago

Vaughn is laying sod in his backyard. A diagram of his backyard is bel ow

Orlov [11]

Answer: $A=944\ ft^2$

Step-by-step explanation:

You need to use the following formula that is used to find the area of a trapezoid:

$A=(\frac{M+m}{2})h$

Where "M"and "m" are the bases of the trapezoid and "h" is the height of the trapezoid.

Based on the information given in the exercise, you can identify that:

$M=c=36\ ft\\\\m=a=23\ ft\\\\h=b=32\ ft$

Knowing these values, you can substitute them into the formula:

$A=(\frac{36\ ft+23\ ft}{2})(32\ ft)$

Finally, you must evaluate in order to find its area. This is:

$A=(\frac{59\ ft}{2})(32\ ft)\\\\A=\frac{1888\ ft^2}{2}\\\\A=944\ ft^2$

7 0

3 years ago

Which is the best prediction for the number of pages in a chapter that takes 18 minutes to read?

mario62 [17]

Answer with explanation:

Time taken by a person to read number of pages in a chapter= 18 minutes

It is not given what is the length of the page.So,we can't say exactly how many pages can a person read by completely understading what is written in each page in a chapter.

So, to fully understand each and every page in 18 minutes you can read minimum number of pages from the option given.

Option A:⇒ 15, is most appropriate.

9 0

3 years ago

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Sharon rented a car for a base price of $200 and has to pay $13 for each day she drives. If her total bill is $252, how many day

ollegr [7]

three thousand two handrend and seventy six

3 0

3 years ago

How many cm3 is in 1 liter? i just wondering...

natali 33 [55]

Hello,

1 liter of water in normal conditions has a volume of 1dm^3=(1dm)^3=(10 cm)^3=10^3 cm^3=1000 cm^3

4 0

4 years ago

Y = ___x - ___ Enter the missing numbers separated by a comma and no spaces!

Y = _x - _ Enter the missing numbers separated by a comma and no spaces!