## A PLUS B PLUS C WHOLE SQUARE FORMULA

On this webpage a plus b plus c whole square formula, that is (a + b + c)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.

## a plus b plus c whole square formula

Question 1 :

Expand (5x + 3y + 2z )²

Solution:

Here the question is in the form of (a + b + c) ². Instead of a we have "5x" instead of b we have "3y" and instead of c we have "2z" . So we need to apply this formula.That is a² + b² + c² + 2 ab + 2 bc +2 ca and we need to apply those values instead of a,b and c

= (5x)² + (3y)² + (2z)² + 2 (5x) (3y) + 2 (3y) (2z) + 2 (2z) (5x)

= 5²x² + 3²y² + 2²z² + 2 (15 x y) + 2 (6yz) + 2 (10zx)

= 25 x² + 9 y² + 4 z² + 30 x y + 12yz + 20 z x

Question 2 :

Expand (x - 2y + z ) ²

Solution:

Here the question is in the form of a plus b plus c whole square formula that is (a + b + c) ². Instead of a we have "x" instead of b we have "-2y" and instead of c we have "z" . So we need to apply the formula for squares.That is a² + b² + c² + 2 ab + 2 bc +2 ca and we need to apply those values instead of a,b and c

= (x)² + (-2y)² + (z)² + 2 (x) (-2y) + 2 (-2y) (z) + 2 (z) (x)

= x² + (-2)²y² + z² + 2 (x) (-2y) + 2(-2y) (z) + 2 (z)(x)

= x² + 4y² + z² -4 x y - 4 y z + 2 z x

Question 3 :

If a + b + c = 15 , a b + b c + c a = 25 find a² + b² + c².

Solution:

(a + b + c)² =  a² + b² + c² + 2 ab + 2 bc +2 ca

(a + b + c)² =  a² + b² + c² + 2 (ab + bc + ca)

a² + b² + c² = (a + b + c)² - 2 (ab + bc + ca)

= (15)² - 2 (25)

= 225 - 50

= 175

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(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