Question

(a-2b)^2 - (a-b)(a+b)

Answer 1

(a-2b)^2 - (a-b)(a+b)=а²-4ав+4в²-а²+в²=5в²-4ав

Answer 2

Ответ:

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

Answer 3

Let's simplify the given expression step by step:

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

Step 1: Expand the square of the first term (a-2b)^2 (a-2b)^2 = (a-2b)(a-2b) = a^2 - 2ab - 2ab + 4b^2 = a^2 - 4ab + 4b^2

Step 2: Expand the second term (a-b)(a+b) (a-b)(a+b) = a(a+b) - b(a+b) = a^2 + ab - ab - b^2 = a^2 - b^2

Now the expression becomes:

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

Step 3: Distribute the negative sign into the second term: (a^2 - 4ab + 4b^2) - (a^2 - b^2) = a^2 - 4ab + 4b^2 - a^2 + b^2

Step 4: Combine like terms: a^2 - a^2 = 0 (a^2 cancels out) -4ab + b^2 = b^2 - 4ab

So the simplified expression is: b^2 - 4ab