Question

1-(x^2-2xy+y^2) 1-a^2-2ab-b^2 4+(-x^2-2xy-y^2)

Answer 1

1-(x²-2xy+у²)=1-(х-у)²=(1-(х-у))(1+(х-у))=(1-х+у)(1+х-у)

1-а²-2ab-b²=1-(а²+2ab+b²)=1-(a+b)²=(1-(a+b))(1+(a+b))=(1-a-b)(1+a+b)

4+(-x²-2xy-y²)=4-х²-2ху-у²=4-(х²+2ху+у²)=4-(х+у)²=(2-(х+у))(2+(х+у))=(2-х-у)(2+х+у)

Answer 2

To simplify the expression, let's break it down step by step:

1. 1 - (x^2 - 2xy + y^2): We can simplify the expression inside the parentheses by recognizing it as a perfect square trinomial. It can be rewritten as (x - y)^2. Substituting it back into the original expression, we have: 1 - (x^2 - 2xy + y^2) = 1 - (x - y)^2

2. 1 - a^2 - 2ab - b^2: This expression seems to be a quadratic trinomial. We can rearrange it as follows: (1 - a^2) - 2ab - b^2 = 1 - (a^2 + 2ab + b^2) Recognizing that a^2 + 2ab + b^2 is a perfect square trinomial, it can be rewritten as (a + b)^2: 1 - (a^2 + 2ab + b^2) = 1 - (a + b)^2

3. 4 + (-x^2 - 2xy - y^2): Here, we have a negative quadratic trinomial. To simplify, we can rearrange it as: 4 - x^2 - 2xy - y^2 = (4 - x^2) - 2xy - y^2 The expression inside the parentheses, 4 - x^2, can be further simplified by recognizing it as a difference of squares: (2 - x)(2 + x). Substituting it back into the original expression, we have: (2 - x)(2 + x) - 2xy - y^2 = (2 - x)(2 + x) - 2xy - y^2

So, the simplified forms of the given expressions are:

1. 1 - (x^2 - 2xy + y^2) = 1 - (x - y)^2
2. 1 - a^2 - 2ab - b^2 = 1 - (a + b)^2
3. 4 + (-x^2 - 2xy - y^2) = (2 - x)(2 + x) - 2xy - y^2