On this webpage a cube plus b cube formula, that is (a³+b³) we are going to see some example problems based on this formula.

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

Now let us see the

Expand x³ + 2 ³

Solution:

Here the question is in the form of (a ³ + b ³). Instead of a we have **"x" ** and instead of b we have **"2" **. Now we need to apply the formula **
(a+b)(a² - ab + b²) ** and we need to apply those values instead of a and b

x³ + 2 ³ = (x + 3) ((x)² - x(3) + 3 ²)

= (x+3) (x² - 3x + 9)

There fore the expansion of x³ + 2 ³ is (x+3) (x² - 3x + 9)

Question 2 :

Expand (3x)³ + 4 ³

Solution:

Here the question is in the form of (a ³ + b ³). Instead of a we have **"3x" ** and instead of b we have **"4" **. Now we need to apply the formula **
(a+b)(a² - ab + b²) ** and we need to apply those values instead of a and b

(3x)³ + 4 ³ = (3x + 4) (3x)² - 3x(4) + 4 ²

= (3x+4) ((3 ²x² - (3x)(4) + 4²)

= (3x+4) (9x² - 12x + 16)

There fore the expansion of (3x)³ + 4 ³ is (3x+4) (9x² - 12x + 16)

Actually we have another formula for a³ + b³. We can derive this formula from (a + b)³

(a + b)³ = a³ + 3 a² b + 3 a b² + b³

= a³ + b³+ 3 a b (a + b)

(a + b)³ - 3 a b (a + b) = a³ + b³

a³ + b³ = (a + b)³ - 3 a b (a + b) a cube plus b cube formula

Question 3 :

Find x³ + y³ if x + y = 4 and x y = 5.

Solution:

Here the question is in the form of (a ³ + b ³).

a³ + b³ = (a + b)³ - 3 a b (a + b)

instead of a we have "x" and instead of b we have "y"

x³ + y³ = (x + y)³ - 3 x y (x + y)

= 4³ - 3 (5) (4)

= 64 - 60

= 4

HTML Comment Box is loading comments...

**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**