Question

(5x+3y)²-(2x-y)(4x-9y)

Answer 1

Ответ:

(5x + 3)²- (2x - y)(4x-9y)

(8x)²-(8x²-6xy-4xy+3y²)

64x²-(8x²-6xy - 4xy+3y²)

64x²-(8x²-10xy+3y²)

64x²-8x²+10xy-3y²

64x²-8x²

(64 - 8)x²=56²

56x²+10xy-3y²

Answer 2

To simplify the given expression, let's expand each term and then combine like terms:

Given expression: (5x+3y)² - (2x-y)(4x-9y)

First, let's expand the square of the binomial (5x+3y)²:

(5x+3y)² = (5x+3y)(5x+3y) = 25x² + 15xy + 15xy + 9y² = 25x² + 30xy + 9y²

Now, let's expand the product of the two binomials (2x-y)(4x-9y):

(2x-y)(4x-9y) = 2x(4x) - 2x(9y) - y(4x) + y(9y) = 8x² - 18xy - 4xy + 9y² = 8x² - 22xy + 9y²

Now, substitute these expanded forms back into the original expression:

(5x+3y)² - (2x-y)(4x-9y) = (25x² + 30xy + 9y²) - (8x² - 22xy + 9y²)

Now distribute the negative sign to every term inside the second parentheses:

= 25x² + 30xy + 9y² - 8x² + 22xy - 9y²

Now combine like terms:

= (25x² - 8x²) + (30xy + 22xy) + (9y² - 9y²) = 17x² + 52xy

So, the simplified expression is: 17x² + 52xy