Question

(6x+5y)^2-8(2x-3y)^2Помогите.....​

Answer 1

Ответ:

$4 {x}^{2} + 156xy - 47 {y}^{2}$

Пошаговое объяснение:

1) Разложить выражения:

$36 { {x}^{} }^{2} + 60xy + 25 {y}^{2} - 8(4 {x}^{2} - 12xy + 9 {y}^{2} )$

2) Раскрыть скобки, выполнив умножение на -8:

$36 {x}^{2} + 60xy + 25 {y}^{2} - 32 {x}^{2} + 96xy - 72 {y}^{2}$

3) Привести подобные члены:

$4 {x}^{2} + 156xy - 47 {y}^{2}$

Answer 2

Ответ:

(6х+5у)^2-8(2х-3у)^2=36х^2+60ху+25у^2-8(4х^2-

-12ху+9у^2)=36х^2+60ху+25у^2-32х^2+96ху-

-72у^2=4х^2+156ху-47у^2

Answer 3

Sure, I'd be happy to help you simplify the expression!

Let's start by expanding the given expression step by step:

1. Begin with the expression: (6x + 5y)^2 - 8(2x - 3y)^2

2. Expand the first square: (6x + 5y)^2 = (6x + 5y)(6x + 5y)

   Use the FOIL method to expand: (6x + 5y)(6x) + (6x + 5y)(5y)

   Expanding further: 36x^2 + 30xy + 30xy + 25y^2

   Simplify: 36x^2 + 60xy + 25y^2

3. Expand the second square: (2x - 3y)^2 = (2x - 3y)(2x - 3y)

   Again, use the FOIL method: (2x - 3y)(2x) + (2x - 3y)(-3y)

   Expanding further: 4x^2 - 6xy - 6xy + 9y^2

   Simplify: 4x^2 - 12xy + 9y^2

4. Now substitute the expanded expressions back into the original expression:

   (6x + 5y)^2 - 8(2x - 3y)^2

   = (36x^2 + 60xy + 25y^2) - 8(4x^2 - 12xy + 9y^2)

5. Distribute the negative 8 to each term inside the second parenthesis:

   = 36x^2 + 60xy + 25y^2 - 32x^2 + 96xy - 72y^2

6. Combine like terms:

   = (36x^2 - 32x^2) + (60xy + 96xy) + (25y^2 - 72y^2)

   = 4x^2 + 156xy - 47y^2

So, the simplified expression is 4x^2 + 156xy - 47y^2.