FORMULA FOR A MINUS B WHOLE SQUARE

On this webpage formula for a minus b whole square, that is (a-b)²  we are going to see some example problems based on this formula.

What is Algebraic identity?

An identity is an equality that remains true regardless of the values of any variables that appear within it.

Now let us see the

Formula For a Minus b Whole Square

Question 1:

Expand (2x - 3) ²

Solution:

Here the question is in the form of (a-b) ². Instead of a we have "2x" and instead of b we have "3" . Now we need to apply the formula a² - 2ab + b ² and we need to apply those values instead of a and b

(2x - 3)² = (2x)² - 2 (2x) (3) + (3)²

= 4x² - 12 x + 9

Question 2 :

Expand (x - 5) ²

Solution:

Here the question is in the form of (a-b) ². Instead of a we have "x" and instead of b we have "5" . Now we need to apply the formula a² - 2ab + b ² and we need to apply those values instead of a and b

(x - 5)² = (x)² - 2 (x) (5) + (5)²

= x² - 10 x + 25

Question 3 :

Expand (3x - 7) ²

Solution:

Here the question is in the form of (a-b) ². Instead of a we have "3x" and instead of b we have "7" . Now we need to apply the formula for a minus b whole square that is  a² - 2ab + b ² and we need to apply those values instead of a and b

(3x - 7)² = ( 3 x )² - 2 ( 3 x ) ( 7 ) + ( 7 )²

= 3²x² - 6 x ( 7 ) + 49

= 9 x² - 42 x + 49

Question 4 :

[√2 - (1/√ 2)]²  is equal to

Solution:

(a - b)² = a² + b² - 2 a b

a = √2  b = 1/√2

[√2 - (1/√ 2)]² = ( √2 )² + (1/√2)² - 2 √2 (1/√2)

= 2 + (1/2) - 2

= (1/2)

We are using this formulas in many of the problems in algebra.We can easily memo rise this by reading this formula by comparing.

(a - b)² = a² - 2 ab + b²

a² - b² = (a + b) (a - b)

(x+a)(x+b)=x²+(a+b)x+ab

(a+b)³=a³+3a²b+3ab²+b³

(a-b)³=a³-3a²b+3ab²-b³

(a³+b³)= (a+b)(a²-ab+b²)

(a³-b³)=(a-b)(a²+ab+ b²)

(a+b+c)²= a²+b²+c²+2ab+2bc+2ca