Which of the following is correct?
- A(4x−5y)
2
=16x
2
−20xy+25y
2 - B(4x−5y)
2
=16x
2
+40xy−25y
2 - C(4x−5y)
2
=16x
2
−40xy+25y
2 - D(4x−5y)
2
=16x
2
−20xy−25y
2
Solution & Step-by-step Explanation
Using the standard algebraic identity:
(a−b)
2
=a
2
−2ab+b
2
Here, let a=4x and b=5y. Substituting these values into the formula, we get:
(4x−5y)
2
=(4x)
2
−2(4x)(5y)+(5y)
2
(4x−5y)
2
=16x
2
−40xy+25y
2
Thus, option C is the correct equation.
(a−b)
2
=a
2
−2ab+b
2
Here, let a=4x and b=5y. Substituting these values into the formula, we get:
(4x−5y)
2
=(4x)
2
−2(4x)(5y)+(5y)
2
(4x−5y)
2
=16x
2
−40xy+25y
2
Thus, option C is the correct equation.