Question

Спростіть вираз: (–а + 2b)^2 + (a + 2b)^2 СРОЧНО!! Буду очень благодарна)

Answer 1

$(-a+2b)^{2}+(a+2b)^{2} \\ (2b-a)^{2} +a^{2}+4ab+4b^{2} \\ 4b^{2}-4ab+a^{2}+a^{2}+4ab+4b^{2}\\ 8b^{2}+2a^{2} \\ ------------------------------------\\ Otvet: 8b^{2}+2a^{2}$

Answer 2

Simplifying the Expression: (-a + 2b)^2 + (a + 2b)^2

To simplify the given expression (-a + 2b)^2 + (a + 2b)^2, we can use the formula for expanding the square of a binomial expression, which is (x + y)^2 = x^2 + 2xy + y^2.

First, let's expand each term in the given expression:

1. Expand (-a + 2b)^2: - Using the formula (x + y)^2 = x^2 + 2xy + y^2, we get: - (-a + 2b)^2 = (-a)^2 + 2*(-a)*(2b) + (2b)^2

2. Expand (a + 2b)^2: - Using the same formula, we get: - (a + 2b)^2 = a^2 + 2*a*2b + (2b)^2

Now, let's simplify each of these expanded expressions.

Simplified Expression

After expanding and simplifying the given expression, we get:

(-a + 2b)^2 + (a + 2b)^2 = a^2 + 4ab + 4b^2 + a^2 + 4ab + 4b^2

Simplifying further, we combine like terms:

(-a + 2b)^2 + (a + 2b)^2 = 2a^2 + 8ab + 8b^2

So, the simplified form of the given expression (-a + 2b)^2 + (a + 2b)^2 is 2a^2 + 8ab + 8b^2.