Question

(2x-1)^2 По формуле а^2+2ab+b^2

Answer 1

Пошаговое объяснение:

(2x-1)²=(2x)²-2•2x•1+1²=4x²-4x+1

Answer 2

To expand the expression (2x - 1)^2 using the formula (a^2 + 2ab + b^2), we can treat (2x - 1) as 'a' and then apply the formula:

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

Here, a = (2x - 1), b = (2x - 1)

Now, let's plug these values into the formula:

(2x - 1)^2 = (a^2 + 2ab + b^2)

= ((2x - 1)^2 + 2(2x - 1)(2x - 1) + (2x - 1)^2)

Now, let's calculate each term:

1. (2x - 1)^2 = (2x - 1)(2x - 1) Applying the FOIL method (First, Outer, Inner, Last): = 4x^2 - 2x - 2x + 1 = 4x^2 - 4x + 1

2. 2(2x - 1)(2x - 1) = 2(4x^2 - 4x + 1) = 8x^2 - 8x + 2

3. (2x - 1)^2 = (2x - 1)(2x - 1) (same as the first term) = 4x^2 - 4x + 1

Now, let's put it all together:

(2x - 1)^2 = (4x^2 - 4x + 1) + 2(4x^2 - 4x + 1) + (4x^2 - 4x + 1)

To simplify, combine like terms:

(2x - 1)^2 = 4x^2 - 4x + 1 + 8x^2 - 8x + 2 + 4x^2 - 4x + 1

Now, combine the terms with the same power of x:

(2x - 1)^2 = (4x^2 + 8x^2 + 4x^2) + (-4x - 8x - 4x) + (1 + 2 + 1)

Add the coefficients:

(2x - 1)^2 = 16x^2 - 16x + 4

So, the expanded form of (2x - 1)^2 using the formula (a^2 + 2ab + b^2) is 16x^2 - 16x + 4.