Question

What is the factored form of x^2 + 4xy - 21y^2?

A. xy(x + 4 - 21y)
B. (x - 3y)(x + 7y)
C. x(x + 4y) + y(4x - 21y)
D. (x + 3y)(x - 7y)

Answer 1

The factored form of the quadratic equation x^2 + 4xy - 21y^2 is (x + 7y)(x - 3y), which is option B in the multiple-choice question.

Step-by-step explanation:

The factored form of the quadratic equation x^2 + 4xy - 21y^2 is determined by finding two numbers that multiply to -21y^2 and add to 4y. After examining the possible factors of -21y^2, we discover that 7y and -3y are the numbers that work because (7y) * (-3y) = -21y^2 and (7y) + (-3y) = 4y.

Therefore, the equation factors into (x + 7y)(x - 3y), which corresponds to option B.