Question

$(x + y)(x - y)$
​

Answer 1

Answer:

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Step-by-step explanation:

$(x + y)(x - y) = x^{2} - {y}^{2}$

Answer 2

Step-by-step explanation:

This is an example of the perfect square. The formula for this is:

(

a

+

b

)

(

a

+

b

)

=

a

2

+

2

a

b

+

b

2

Substituting

x

for

a

and

y

for

b

gives:

(

x

+

y

)

(

x

+

y

)

=

x

2

+

2

x

y

+

y

2

Another way to show this is the correct answer is as follows:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

(

x

+

y

)

(

x

+

y

)

becomes:

(

x

×

x

)

+

(

x

×

y

)

+

(

y

×

x

)

+

(

y

×

y

)

x

2

+

x

y

+

x

y

+

y

2

We can now combine like terms:

x

2

+

1

x

y

+

1

x

y

+

y

2

x

2

+

(

1

+

1

)

x

y

+

y

2

x

2

+

2

x

y

+

y

2