Question

(x-y)^2-(m+n)^2=(2a-3c)^2+(4b+5d)^2=​

Answer 1

1)

Если нужно упростить:

$\displaystyle \tt (x-y)^2-(m+n)^2=x^2-2xy+y^2-(m^2+2mn+n^2)=\boxed{\bold{x^2-2xy+y^2-m^2-2mn-n^2}}$

Если нужно разложить на множители:

$\displaystyle \tt (x-y)^2-(m+n)^2=(x-y-(m+n))(x-y+(m+n))=\boxed{\bold{(x-y-m-n)(x-y+m+n)}}$

2)

$\displaystyle \tt (2a-3c)^2+(4b+5d)^2=\boxed{\bold{4a^2-12ac+9c^2+16b^2+40bd+25d^2}}$

Answer 2

The expression you provided is:

(x - y)^2 - (m + n)^2 = (2a - 3c)^2 + (4b + 5d)^2

This equation represents two separate equations. Let's break it down:

Equation 1: (x - y)^2 - (m + n)^2 = 0

This equation states that the square of the difference between x and y is equal to the square of the sum of m and n.

Equation 2: (2a - 3c)^2 + (4b + 5d)^2 = 0

This equation states that the sum of the squares of 2a minus 3c and 4b plus 5d is equal to zero.

Please note that without specific values or additional information, it is not possible to determine the exact solutions or simplify the equations further. If you provide more context or any specific values for the variables involved, I can assist you further.