On this webpage "expanding brackets with powers of 2", we are going to see how to expand algebraic expressions of power 2.

An identity is an equality that remains true regardless of the values of any variables that appear within it.

**Question 1 :**

Expand (5x + 3)²

**Solution :
**

Here the given question is in the form of (a+b)². Instead of a we have **"5x" **and** **instead of b we have **"3" **.

So we need to apply the formula ** a² + 2ab + b² ** and we need to apply those values of a and b

a = 5 x and b = 3

(5x + 3)² = (5x)² + 2 (5x) (3) + (3)²

= 25x² + 30 x + 9

= 25x² + 30 x + 9

Let us see the next example problem on "Expanding brackets with powers of 2".

**Question 2 :**

Expand (x + 2)²

**Solution :**

Here the question is in the form of (a+b)². Instead of a we have **"x" ** and instead of b we have **"2".**

So we need to apply the formula ** a² + 2ab + b ² ** and we need to apply those values of a and b

a = x and b = 2

(x + 2)² = (x)² + 2 (x) (2) + (2)²

= x² + 4 x + 4

Let us see the next example problem on "Expanding brackets with powers of 2".

**Question 3 :**

(105)² is equal to

**Solution :**

Instead of multiplying 105 x 105 to get the value of (105)² we can use algebraic formula for a plus b whole square that is (a+b)² to get the same answer.105 can be written as 100 + 5.

(105)² = (100 + 5)²

(a + b)² = a² + b² + 2 a b

a = 100 b = 5

(105)² = (100)² + (5)² + 2 (100)(5)

= 10000 + 25 + 1000

= 11025

Let us see the next example problem on "Expanding brackets with powers of 2".

**Question 4 :**

Expand (2x - 3) ²

**Solution :**

Here the question is in the form of (a-b) ². Instead of a we have **"2x" **and instead of b we have **"3" **. Now we need to apply the formula **a² - 2ab + b ² **and we need to apply those values instead of a and b

(2x - 3)² = (2x)² - 2 (2x) (3) + (3)²

= 4x² - 12 x + 9

Let us see the next example problem on "Expanding brackets with powers of 2".

**Question 5 :**

Expand (x - 5) ²

**Solution :**

Here the question is in the form of (a-b) ². Instead of a we have **"x" **and instead of b we have **"5" **. Now we need to apply the formula **a² - 2ab + b ² **and we need to apply those values instead of a and b

(x - 5)² = (x)² - 2 (x) (5) + (5)²

= x² - 10 x + 25

Let us see the next example problem on "Expanding brackets with powers of 2".

**Question 6 :**

Expand (3x - 7) ²

**Solution :**

Here the question is in the form of (a-b) ². Instead of a we have **"3x" **and instead of b we have **"7" **. Now we need to apply the formula for a minus b whole square that is **a² - 2ab + b ² **and we need to apply those values instead of a and b

(3x - 7)² = ( 3 x )² - 2 ( 3 x ) ( 7 ) + ( 7 )²

= 3²x² - 6 x ( 7 ) + 49

= 9 x² - 42 x + 49

Let us see the next example problem on "Expanding brackets with powers of 2".

**Question 7 :**

Expand (5x)² - 3 ²

**Solution :**

Here the question is in the form of (a²- b²) . Instead of a we have **"5x" **and instead of b we have **"3" **. So we need to apply the formula **(a + b) (a - b) **and we need to apply those values instead of a and b

(5x)² - 3² = (5x + 3) (5x - 3)

Let us see the next example problem on "Expanding brackets with powers of 2".

**Question 8 :**

Expand x² - 1 ²

**Solution :**

Here the question is in the form of (a²-b²) ². Instead of a we have **"x" **and instead of b we have **"1" **. So we need to apply the formula for square .That is **(a+b)(a-b) **and we need to apply those values instead of a and b

x² - 1² = (x + 1) (x-1)

Let us see the next example problem on "Expanding brackets with powers of 2".

**Question 9 :**Expand 16 x² - 9

We can split the first term 16 as 4x4 and 9 as 3x3. Instead of this we can write

= 4 ²x² - 3²

= (4x)² - 3 ²

= (4x + 3) (4x - 3)

**Question 10 :**

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+2ab+2bc+2ca **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 11 :**

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

**(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**

We hope that the students would have understood the stuff given on "Expanding brackets with powers of 2"

Apart from the stuff given above, if you want to know more about "Expanding brackets with powers of 2", please click here

If you need any other stuff, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM 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**