Answer:

A square with length a which has an area of a².

2 Rectangles with length a and breadth b which has an area of ab each.

A square with length b which has an area of b².

So the area of the new square with length a + b will be

(a + b)² = (Area of the Square with length a) + (2 X Area of the Rectangle with length a and breadth b) + (Area of the Square with length b)

which can be written as

(a + b)² = a² + 2ab + b²

Hence Proved

Thank you

Appropriate Question :-

factorise each of the following polynomials using (a + b)²= a² + 2ab+ b² and (a - b)² = a² - 2ab + b²

A) 25p²- 50pq+25q²

Solution :- [tex]\\[/tex]

25p² -50pq + 25q²

= (5p)² - 2(5p)(5q) + (5)q²

= 25p² - 50pq + 25q²

We know that,

(a - b)² = a² - 2ab + b²

= (5p - 5q)²

therefore,

25p² - 50pq + 25q² = (5p - 5q)²

For more details Refer :-

https://brainly.in/question/47166999

More Identities :-

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (a + b)³ = a³ + 3a²b + 3ab² + b³
• (a - b)³ = a³ - 3a²b + 3ab² - b³

Hope it helps you :)