Question

(5x-2y)(3x+5y)-(2.5x-3y)(4x+8y)

Answer 1

Ответ:

(5x-2y)(3x+5y)-(2,5x-3y)(4x+8y)=15x²+25xy-6xy-10y²-(10x²+20xy-12xy-24y²)=15x²+25xy-6xy-10y²-10x²-8xy+24y²=5x²+11xy+14y².

Answer 2

To simplify the expression, follow these steps:

Step 1: Expand both parts of the expression.

First, let's expand (5x - 2y)(3x + 5y): (5x)(3x) + (5x)(5y) + (-2y)(3x) + (-2y)(5y)

Now, let's expand (2.5x - 3y)(4x + 8y): (2.5x)(4x) + (2.5x)(8y) + (-3y)(4x) + (-3y)(8y)

Step 2: Simplify each term:

Expanding the first part: (5x)(3x) = 15x^2 (5x)(5y) = 25xy (-2y)(3x) = -6xy (-2y)(5y) = -10y^2

Expanding the second part: (2.5x)(4x) = 10x^2 (2.5x)(8y) = 20xy (-3y)(4x) = -12xy (-3y)(8y) = -24y^2

Step 3: Combine like terms:

(15x^2 + 25xy - 6xy - 10y^2) - (10x^2 + 20xy - 12xy - 24y^2)

Step 4: Perform subtraction:

Combine the terms inside the brackets and change the sign of each term in the second set of brackets:

(15x^2 + 25xy - 6xy - 10y^2) - 10x^2 - 20xy + 12xy + 24y^2

Step 5: Simplify further:

Combine like terms again:

15x^2 + 25xy - 6xy - 10y^2 - 10x^2 - 20xy + 12xy + 24y^2

Step 6: Continue simplification:

Combine the terms containing x^2: (15x^2 - 10x^2) = 5x^2 Combine the terms containing xy: (25xy - 6xy - 20xy + 12xy) = 11xy Combine the terms containing y^2: (-10y^2 + 24y^2) = 14y^2

Final simplified expression:

5x^2 + 11xy + 14y^2