What is the factored form of $x^{2}+4 x y-21 y^{2} ?$
A. $x y(x+4-21 y)$
B. $(x-3 y)(x+7 y)$
C. $x(x+4 y)+y(4 x-21 y)$
D. $(x+3 y)(x-7 y)$

Answer

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Answer

$ \boxed{(x-3 y)(x+7 y)} $

Steps

Step 1 ：Factor the given expression: $x^{2}+4 x y-21 y^{2}$

Step 2 ：Find the factors of the constant term (-21) and check if they satisfy the middle term (4x): $(x-3 y)(x+7 y)$

Step 3 ：$ \boxed{(x-3 y)(x+7 y)} $