Question

What is the factored form of x2 + 4xy – 21y2?

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

Answer 1

`\sf \: {x}^(2) + 4xy - 21 {y}^(2)`

`\sf \: Rewrite \: the \: equation⟹( {x}^(2) - 3xy) + (7xy - 21y {}^(2) )`

`\sf \: 1)( {x}^(2) - 3xy) = x(x - 3y)`

`\sf2) \: (7xy - 21 {y}^(2) ) = 7y(x - 3y)`

`\sf \: Now \: the \: equation \: becomes \: ⟹ \\ \sf \: x(x - 3y) + 7y(x - 3y)`

`\sf \: Factor \: out \: the \: common \: term \: (x - 3y) \\ \sf =( x - 3y) + (x + 7y) \\`

Answer ⟶
`\boxed{\sf {B) (x-3y)(x+7y)}}`