Formula for Squares

In this topic formula for squares we are going to discuss about the formula which are being used to expand the terms like in the form (a + b + c) ². We are going to see some of the example problem.After getting clear of using this you can try the worksheet also.We have given this worksheet for the purpose of making practice.If you practice this worksheets it will become easy to face problems in the topic algebra.We will use these formulas in most of the problem.

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 xy) + 2 (6yz) + 2 (10zx)

       = 25x² + 9y² + 4z² + 30 xy + 12yz + 20 zx

Question 2 :

Expand (x - 2y + z ) ²

Solution:

Here the question is in the form of (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 xy - 4yz + 2 zx

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