Question

Раскрыть скобки (2x-y-3)^2+(x-3y-1)^2

Answer 1

(2x-y-3)²+(x-3y-1)²=(2x-y)²-6(2x-y)+9+

(x-3y)²-2(x-3y)+1=4x²-4xy+y²-12x+6y+9+

x²-6xy+9y²-2x+6y+1=5x²+10y²-10xy-14x+12y+10

Answer 2

To expand the given expression, we'll use the formula for expanding the square of a binomial:

For any binomial (a - b)^2, the expansion is: (a - b)^2 = a^2 - 2ab + b^2

Now let's apply this to the given expression: (2x - y - 3)^2 + (x - 3y - 1)^2

Expanding the first binomial: (2x - y - 3)^2 = (2x)^2 - 2(2x)(y) + (y)^2 - 2(2x)(3) + 2(y)(3) + 3^2 = 4x^2 - 4xy + y^2 - 4x + 6y + 9

Expanding the second binomial: (x - 3y - 1)^2 = (x)^2 - 2(x)(3y) + (3y)^2 - 2(x)(1) + 2(3y)(1) + 1^2 = x^2 - 6xy + 9y^2 - 2x + 6y + 1

Now, putting both expanded expressions back together, we get: (2x - y - 3)^2 + (x - 3y - 1)^2 = (4x^2 - 4xy + y^2 - 4x + 6y + 9) + (x^2 - 6xy + 9y^2 - 2x + 6y + 1)

Combining like terms: (2x - y - 3)^2 + (x - 3y - 1)^2 = 4x^2 - 4xy + y^2 - 4x + 6y + 9 + x^2 - 6xy + 9y^2 - 2x + 6y + 1

Finally, let's simplify and group like terms: (2x - y - 3)^2 + (x - 3y - 1)^2 = 4x^2 + x^2 - 4xy - 6xy + y^2 + 9y^2 - 4x - 2x + 6y + 6y + 9 + 1

Combining like terms once again: (2x - y - 3)^2 + (x - 3y - 1)^2 = 5x^2 - 10xy + 10y^2 - 6x + 12y + 10

So, the expanded form of the given expression is: 5x^2 - 10xy + 10y^2 - 6x + 12y + 10