Elementary Algebra:

Elementary algebra is a branch of the science of calculation like arithmetic. In strategies to teach elementary algebra, we use the symbols to denote the quantities and progressions. The arithmetic has a single definite value, but strategies algebraic symbols have a general and not merely a single definite value. Let see about the identities of strategies to teach elementary algebra.

 

Strategies Algebraic Identities:

 

The followings are some of the algebraic identities using in the elementary algebra.

  • (a+b)2= a²+ 2ab + b²
  • (a-b)2= a²- 2ab + b²
  • (a+b) (a-b) = a²- b²
  • (x+a)(x+b) = x² + (a+b) x+ab

 Let see the examples of strategies to teach elementary algebra.

 

Examples of Strategies to Teach Elementary Algebra:

 

1. Expand: (2x + 3y+ 4z)2

Solution:

           Comparing the given expression (2x + 3y+ 4z)2 with (a +b +c)2.

            Then we have,

            a= 2x

            b= 3y

            c=4z

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

            Therefore (2x + 3y+ 4z)2  = (2x)2 + (3y)2 + (4z)2 +2(2x) (3y) +2(3y) (4y) + 2(4x) (2x)

             = 4x2 + 9y2 + 16z2 +12xy +24yz +16zx

2. Find the cube of 4x-5y.

Solution:

             We know that (a -b) 3 = a3 - b3 -3ab (a-b)

             Here, a = 4x,

             b = 5y

            (4x-5y)3 = (4x)3 - (5y) -3* 4x * 5y (4x – 5y)

            = 64x3 - 125y3 -60xy (4x- 5y).

3. Evaluate: 102³ using suitable identity.

Solution:

             1023 = (100 +2)3

             Use the identity (a + b)3 = a3 + b3 + 3ab (a + b)

             Therefore, 1023 = (100 + 2)3

             = 1003 +23 +3* 100* 2(100+ 2)

             = 1000000 + 8 + 600(100 +2)

             = 1000000 + 8 + 60000 + 1200

             = 1061208

 

4. Evaluate 3x² - y² - z if x = 3, y = -1 and z = -2

Solution:

             Substitute the values for the variables.
             = 3(3)2 - (-1)2 - (-2)

             = 3(9) - (1) - (-2)

             = 27 - (1) + (2)

             = 26 + 2

             = 28

             These are the examples of strategies to teach elementary algebra.