Question

Sadie uses the polynomial identity (2x + y)² = 4x² + 4xy + y² to show that 23²= 529. What values can Sadie use for x and y?

A. x = 8 and y = 15
B. x = 8 and y = 7
C. x = 15 and y = 8
D. x = 7 and y = 8 ​

Answer 1

To show that (2x + y)² = 4x² + 4xy + y², we can expand the left side of the equation and substitute the given values of x and y. The correct values for x and y are x = 23 and y = -23.

Step-by-step explanation:

To show that (2x + y)² = 4x² + 4xy + y², we can expand the left side of the equation:

(2x + y)² = (2x + y)(2x + y) = 4x² + 2xy + 2xy + y² = 4x² + 4xy + y²

Now we can substitute the values of x and y given in the question into the expanded equation:

(2(23) + y)² = 4(23)² + 4(23)y + y²

Simplifying this equation gives:

(46 + y)² = 529

Since 46 + y = 23, we can solve for y by subtracting 46 from both sides:

y = 23 - 46 = -23

So the values Sadie can use for x and y are x = 23 and y = -23. Therefore, none of the given options A, B, C, and D are correct.