**Applying the identities :**

Here we are going to see how to apply the algebraic identities to find the expansion of the algebraic expression.

(a + b)² = a² + 2 ab + b²

(a - b)² = a² - 2 ab + b²

a^{2} - b^{2} = (a + b) (a - b)

(x + a) (x + b) = x^{2} + (a + b) x + ab

(a + b)^{3} = a^{3} + 3a^{2}b + 3ab2 + b3

(a - b)^{3} = a^{3} - 3a^{2}b + 3ab^{2} - b^{3}

(x + a) (x + b) = x^{2 }+ (a + b) x + ab

a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})

a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})

Now let us look into some example problems based on the above identities.

**Example 1 :**

Use the suitable identity to find the product of the following

(2x - 5) (2x - 5)

**Solution :**

Instead of writing (2x - 5) two times, we may write it as (2x - 5)^{2}

a = 2x, b = 5

The formula for (a - b)^{2 }is a^{2} - 2ab + b^{2}

(2x - 5)^{2} = (2x)^{2} - 2 (2x) (5) + 5^{2}

= 4x^{2} - 20x + 25

**Example 2 :**

Use the suitable identity to find the product of the following

(2l + 3m) (2l - 3m)

**Solution :**

The given question is in the form (a + b) (a - b)

(a + b) (a - b) = a^{2} - b^{2}

(2l + 3m) (2l - 3m) = (2l)2 - (3m)2

= 2^{2}l^{2} - 3^{2}m^{2}

= 4l^{2} - 9m^{2}

**Example 3 :**

Use the suitable identity to find the product of the following

(8x - 5) (8x + 3)

**Solution :**

The given question is in the form (x + a)(x + b)

(x + a) (x + b) = x^{2} + (a + b) x + ab

x = 8x, a = -5 and b = 3

= (8x)^{2} + (-5 + 3) (8x) + (-5)(3)

= 8^{2}x^{2} + (-2) (8x) - 15

= 64x^{2} - 16x - 15

**Example 4 :**

Use the suitable identity to find the product of the following

96 x 104

**Solution :**

96 = (100 - 4)

104 = (100 + 4)

96 x 104 = (100 - 4) (100 + 4)

The above expression exactly matches (100-4)(100+4)

= 1002 - 42

= 10000 - 16

= 9984

**Example 5 :**

If the values of (a-b) and ab are 6 and 40 respectively, find the values of a^{2} + b^{2} and (a + b)^{2}

**Solution :**

a - b = 6 and ab = 40

(a - b)^{2} = a^{2} - 2ab + b^{2}

Add 2ab on both sides

(a - b)^{2} + 2ab = a^{2} - 2ab + b^{2} + 2ab

a^{2} + b^{2} = (a - b)^{2} + 2ab

= (6)^{2} + 2(40)

= 36 + 80

= 116

After having gone through the stuff given above, we hope that the students would have understood "Applying the identities"

Apart from the stuff given above, if you want to know more about "Applying the identities", please click here

Apart from the stuff "Applying the identities", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**