Question

If (a + b) = 2 and (a - b) = 10, find the values of:
(i) (a² + b²)
(ii) ab

Use the formulas (a + b)² + (a - b)² = 2(a² + b²) and (a + b)² - (a - b)² = 4ab​

Answer 1

Answer:

Given,Simplify (a + b) ² - (a - b) ²?

So first,

(a + b)² = a² + 2ab + b²

(a – b)² = a² – 2ab + b²

(a + b)² – (a – b)² = (a² + 2ab + b²) – (a² – 2ab + b²)

While subtracting polynomials, the signs in the first polynomial are unchanged when the parentheses are dropped, whereas the middle – sign distributes to all of the terms in the second polynomial, thus changing all the signs in the second polynomial when the parentheses are dropped

(a² + 2ab + b²) – (a² – 2ab + b²) = a² + 2ab + b² – a² + 2ab – b²

Rearrange the terms and you get:

a² – a² + 2ab + 2ab + b² – b²

Cancel out same terms with opposite signs, and you get:

2ab + 2ab

which simplifies to our final answer:

4ab