Answer:The answer is choice B
Step-by-step explanation: (3x-2y)2-(2x-3y)2
Final result :
5 • (x + y) • (x - y)
Step by step solution :
Step 1 :
1.1 Evaluate : (3x-2y)2 = 9x2-12xy+4y2
1.2 Evaluate : (2x-3y)2 = 4x2-12xy+9y2
Step 2 :
Pulling out like terms :
2.1 Pull out like factors :
5x2 - 5y2 = 5 • (x2 - y2)
Trying to factor as a Difference of Squares :
2.2 Factoring: x2 - y2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (x + y) • (x - y)
Final result :
5 • (x + y) • (x - y)