VJesus12 wrote:Which expression is equivalent to (5x − 3y)^2?
A. 10x − 6y
B. 25x − 9y
C. 25x^2 − 9y^2
D. 25x^2 − 15xy + 9y^2
E. 25x^2 − 30xy + 9y^2
One option is to use the FOIL method to expand the product (that's the solution I'd typically use)
However, we can also use this approach:
First recognize that we're looking for an expression that's EQUIVALENT to (5x − 3y)^2
for all values of x and y
So, for example, let's determine the value of (5x − 3y)^2 when x = 0 and y = 1
Take (5x − 3y)^2 and replace x with 0 and y with 1 to get: [5(0) − 3(1)]^2 = [−3]^2 =
9
So, the answer choice that's EQUIVALENT to (5x − 3y)^2 must also evaluate to be
9 when x = 0 and y = 1
Let's check each answer choice...
A. 10(0) − 6(1) =
-6. ELIMINATE
B. 25(0) − 9(1) =
-9. ELIMINATE
C. 25(0^2) − 9(1^2) =
-9. ELIMINATE
D. 25(0^2) − 15(0)(1) + 9(1^2) =
9. KEEP
E. 25(0^2) − 30(0)(1) + 9(1^2) =
9. KEEP
Okay, we have two possible answer choices remaining.
We need to plug in ANOTHER set of values.
How about x = 1 and y = 1
Take (5x − 3y)^2 and replace x with 1 and y with 1 to get: [5(1) − 3(1)]^2 = [2]^2 =
4
Let's check the two remaining answer choices...
D. 25(1^2) − 15(1)(1) + 9(1^2) =
19. ELIMINATE
E. 25(1^2) − 30(1)(1) + 9(1^2) =
4. KEEP
Answer: E
Cheers,
Brent
