Question

1) (a+b)^ 2 -c^ 2 ; 2) (m-n)^ 2 -k^ 2 ; 3) (a+2b)^ 2 -9a^ 2 ; 4) (3x - y) ^ 2 - 4y ^ 2 .

Answer 1

Ответ:

1)(a+b-c)*(a+b+c)

2)(m-n-k)*(m-n-k)

3)-4(a-b)*(2a+b)

4)3(x-y)*(3x+y)

Answer 2

Let's simplify each expression:

1. (a+b)^2 - c^2: Expanding the square of a binomial, we have: (a+b)^2 = a^2 + 2ab + b^2

Substituting this back into the expression: (a+b)^2 - c^2 = (a^2 + 2ab + b^2) - c^2 = a^2 + 2ab + b^2 - c^2

2. (m-n)^2 - k^2: Expanding the square of a binomial, we have: (m-n)^2 = m^2 - 2mn + n^2

Substituting this back into the expression: (m-n)^2 - k^2 = (m^2 - 2mn + n^2) - k^2 = m^2 - 2mn + n^2 - k^2

3. (a+2b)^2 - 9a^2: Expanding the square of a binomial, we have: (a+2b)^2 = a^2 + 4ab + 4b^2

Substituting this back into the expression: (a+2b)^2 - 9a^2 = (a^2 + 4ab + 4b^2) - 9a^2 = a^2 + 4ab + 4b^2 - 9a^2

4. (3x - y)^2 - 4y^2: Expanding the square of a binomial, we have: (3x - y)^2 = (3x)^2 - 2(3x)(y) + y^2 = 9x^2 - 6xy + y^2

Substituting this back into the expression: (3x - y)^2 - 4y^2 = (9x^2 - 6xy + y^2) - 4y^2 = 9x^2 - 6xy + y^2 - 4y^2

These are the simplified forms of the given expressions.