Translate the following word phrase into an algebraic expression 7 times the difference of y and one

To solve this problem, we just need to change the described expression into a numerical one.

Our answer is 7(y-1).

This is because the difference of y and 1 refers to the operation of subtraction, and this shows us that we need to subtract 1 from the value that is represented by y. The fact that it says 7 times the difference of y and 1 shows us that we must multiply the quantity y-1 and 7 (meaning we must perform the subtraction between y and 1 before the multiplication with 7). This is what indicates to us that we need parentheses, which allow us to perform this operation first, outlined by the rules of PEMDAS referring to the order of operations.

Hope this helps!

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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