Which of the following is correct?
- A(6x+y)(x-6y) = 6x^2+35xy-6y^2
- B(6x+y)(x-6y) = 6x^2-35xy-6y^2
- C(6x+y)(x-6y) = 6x^2-37xy-6y^2
- D(6x+y)(x-6y) = 6x^2+37xy-6y^2
Solution & Step-by-step Explanation
Let's expand the given expression on the left-hand side:
(6x+y)(x−6y)
Distribute the terms:
=6x(x−6y)+y(x−6y)
=6x
2
−36xy+xy−6y
2
Combine the like terms (−36xy and +xy):
=6x
2
−35xy−6y
2
This matches option B.
(6x+y)(x−6y)
Distribute the terms:
=6x(x−6y)+y(x−6y)
=6x
2
−36xy+xy−6y
2
Combine the like terms (−36xy and +xy):
=6x
2
−35xy−6y
2
This matches option B.