The following patterns are made of small squares. write an expression for the number of small squares in pattern n

An expression for the number of small squares in pattern n is .

In the pattern 1:

3 + (3 x 3) + 3 = 15

Number of small squares = 15

In the pattern 2:

3 + (4 x 4) + 3 = 22

Number of small squares = 22

In the pattern 3:

3 + (5 x 5) + 3 =31

Number of small squares = 31

In the pattern n:

Simplify:

Therefore, an expression for the number of small squares in pattern n is .

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Step-by-step explanation:

The picture of the question in the attached figure

we know that

In the pattern 1 there are

In the pattern 2 there are

In the pattern 3 there are

we can write the expression in the form

where

substitute

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

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step-by-step explanation: