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

(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