Question

Expand using appropriate identity (y-√3)²

Answer 1

If we observe carefully it is in the form of (a-b)² identity . So using the same identity will solve the given problem . For that we need to follow the given steps :

1. Find the expansion of The Identity we are going to use.
2. Proper consideration of the values of a and b
3. Substituting the values
4. Simplify

|| ★ || Identity and it's expansion || ★ ||

(a-b)² = a² - 2ab + b²

|| ★ || Values of a and b || ★ ||

• a = y
• b = √3

|| ★ || Substituting the values and simplify || ★ ||

(a-b)² = a² - 2ab + b²

(y-√3)² = (y)² - 2 × y × √3 + (√3)²

(y-√3)² = y² - 2y√3 + 3

Here the value of square and the value of root in root 3 get cancelled to each other leaving the simple value 3 .

So the expansion is :

y² - 2y√3 + 3

Answer 2

Answer :-

• The expansion is y² - 2y√3 + 3.

Given :-

• (y - √3)²

To Find :-

• Expansion of this

Solution :-

Here, it is in the form of (a - b)².

(a - b)² = a² + b² - 2ab

Where

• a = y
• b = √3

Put the values in the formula

(a - b)² = a² + b² - 2ab

→ (y - √3)² = (y)² + (√3)² - 2 × y × √3

→ (y - √3)² = y² + 3 - 2y√3

→ (y - √3)² = y² - 2y√3 + 3

Hence, the expansion is y² - 2y√3 + 3.