Question

1) 4(a-b)^2-(a+b)^2=2) 9(a-b)^2-4(x-y)^2=пазазя))​

Answer 1

1)

Если нужно упростить:

$\displaystyle \tt 4(a-b)^2-(a+b)^2=4(a^2-2ab+b^2)-(a^2+2ab+b^2)=4a^2-8ab+4b^2-a^2-2ab-b^2=\boxed{\displaystyle \tt \textfb{3a^2+3b^2-10ab}}$

Если нужно разложить на множители:

$\displaystyle \tt 4(a-b)^2-(a+b)^2=(a(a-b)-(a+b))(2(a-b)+(a+b))=(2a-2b-a-b)(2a-2b+a+b)=\fbox{\textbf{(a\:-\:3b)(3a\:-\:b)}}$

2)

Если нужно упростить:

$\displaystyle \tt 9(a-b)^2-4(x-y)^2=9(a^2-2ab+b^2)-4(x^2-2xy+y^2)=\boxed{\displaystyle \tt 9a^2-18ab+9b^2-4x^2+8xy-4y^2}$Если нужно разложить на множители:

$\displaystyle \tt 9(a-b)^2-4(x-y)^2=(3(a-b)-2(x-y))(3(a-b)+2(x-y))=\fbox{\textbf{(3a-3b-2x+2y)(3a-3b+2x-2y)}}$

Answer 2

Let's solve each equation step by step:

1. 4(a - b)^2 - (a + b)^2

Expanding the squared terms: = 4(a^2 - 2ab + b^2) - (a^2 + 2ab + b^2)

Simplifying the expression: = 4a^2 - 8ab + 4b^2 - a^2 - 2ab - b^2

Combining like terms: = 3a^2 - 10ab + 3b^2

So, the simplified expression is 3a^2 - 10ab + 3b^2.

2. 9(a - b)^2 - 4(x - y)^2

Expanding the squared terms: = 9(a^2 - 2ab + b^2) - 4(x^2 - 2xy + y^2)

Simplifying the expression: = 9a^2 - 18ab + 9b^2 - 4x^2 + 8xy - 4y^2

Combining like terms: = 9a^2 - 4x^2 - 18ab + 8xy + 9b^2 - 4y^2

So, the simplified expression is 9a^2 - 4x^2 - 18ab + 8xy + 9b^2 - 4y^2.

Please note that the given expressions do not have any values assigned to the variables, so the expressions are simplified as far as possible without any further evaluation.