Question

A (a+b)– b (a - b) = a² +b²​

Answer 1

Объяснение:

a^2+ab-ba+b^2=a^2+b^2

a^2+b^2=a^2+b^2

сокращаем аb и -ba, так как рни противоположны

Answer 2

Let's simplify the expression step by step to verify if it indeed equals a² + b².

Starting with the given expression:

A(a + b) - b(a - b)

Now, let's use the distributive property to expand the terms:

A * a + A * b - b * a + b * b

Next, combine like terms:

(A * a - b * a) + A * b + b * b

Now, factor out 'a' from the first two terms:

a(A - b) + A * b + b * b

Now, we can see that the first two terms have a common factor of 'a.' Let's factor it out:

a(A - b) + b(A + b)

Now, let's distribute 'a' and 'b' back into the parentheses:

a * A - a * b + b * A + b * b

Now, simplify the terms inside the parentheses:

Aa - ab + Ab + b²

Notice that 'Aa' and 'Ab' are like terms because they both involve 'A.' Let's combine them:

Aa + Ab - ab + b²

Now, we can see that 'Aa' and 'Ab' also have a common factor of 'A.' Let's factor it out:

A(a + b) - ab + b²

At this point, we've simplified the expression as much as possible, and it doesn't equal a² + b². The simplified form is:

A(a + b) - ab + b²

So, the given expression does not equal a² + b².