Question

Раскрыть скобки (2а+b+3c-4b)^2

Answer 1

Вроде бы так)))))))))

Answer 2

To expand the expression (2a + b + 3c - 4b)^2, we use the formula for expanding the square of a binomial:

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

In this case, the binomial is (2a + b + 3c - 4b). Let's proceed with the expansion:

(2a + b + 3c - 4b)^2

To square this binomial, we'll multiply it by itself:

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

Now, let's multiply each term in the first binomial by each term in the second binomial:

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

Now, simplify each term:

4a^2 + 2ab + 6ac - 8ab + 2ab + b^2 + 3bc - 4b^2 + 6ac + 3bc + 9c^2 - 12bc + -8ab - 4b^2 - 12bc + 16b^2

Combining like terms:

4a^2 + 2ab + 6ac - 8ab + 2ab + b^2 + 3bc - 4b^2 + 6ac + 3bc + 9c^2 - 12bc + -8ab - 4b^2 - 12bc + 16b^2

Now, collect like terms and simplify further:

4a^2 + b^2 + 9c^2 + (2ab - 8ab - 8ab) + (6ac) + (3bc - 12bc - 12bc)

The like terms inside the parentheses can be combined:

4a^2 + b^2 + 9c^2 - 14ab - 6bc

So, the fully expanded form of (2a + b + 3c - 4b)^2 is:

4a^2 + b^2 + 9c^2 - 14ab - 6bc