The square of 356 is 126,736 and the square of 357 is 127,449. What is 3582? Try to solve this problem without multiplying. Show your work.

The problem to get 358² is solved by adding 357 twice and then add 1 to the value of 357²

Step-by-step explanation:

The given information are;

The square of 356 = 126,736

The square of 357 = 127,449

We note that 357² = (356 + 1)² = 356² + 2×356 + 1 = 126,763 + 712 + 1 = 127,449

We can write the above equation as follows;

357² = (356 + 1)² = 356² + 356 + 356 + 1 = 126,763 + 712 + 1 = 127,449

357² = 127,449

Similarly, we have;

358² = (357 + 1)² = 357² + 357 + 357 + 1 = 128,164

358² =  128,164

We can also look at the question as forming squares with tiles

To form the square tile with 358 units per side, we add an extra row and column of 357 tiles each. Completing the figure with an extra tile at the top right or left corner

Therefore, the area of the 358 unit per side square = The area of the 357 unit per side + 357 + 357 + 1 =  128,164

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:

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.