Question

Упростите выражение (2х+3у)²-(3у-2х)²

Answer 1

1 сп.

$(2x + 3y)^{2} - (3y - 2x)^{2} = (2x + 3y - 3y + 2x)(2x + 3y + 3y - 2x) = \\ = 4x \times 6y = 24xy$

2 сп.

${(2x + 3y)}^{2} - {(3y - 2x)}^{2} = 4 {x}^{2} + 12xy + 9 {y}^{2} - (9 {y}^{2} - 12xy + 4 {x}^{2} ) = \\ ={4x}^{2} + 12xy + 9 {y}^{2} - 9 {y}^{2} + 12xy - 4 {x}^{2} = 24xy$