A Cube Plus B Cube Formula

a cube plus b cube formula

a3 + b3 is the formula of the sum of cubes of the two numbers. The sum of cubes of the two numbers is also known as the formula of a3 + b3. 

• This is an algebraic formula that can factorise the numbers. 
• An algebraic equation depicts a scale done on one side of the scale with a number that is also done on either side of the scale.
• In algebraic expressions the numbers are constants.
• In algebra we substitute the number with letters or alphabets to solve the problem.
• To identify the quantities in the equations we can use the letters like x,y,a,b etc.
• The formula is:-

a3 + b3 = (a+b)(a2 – ab + b2)

Example 8×3 + 27y3

8×3 + 27y3 =(2x)3 + (3y)3

a3 + b3 = (a+b)(a2 – ab – b2)

= (2x+ 3y)[(2x)2 – (2x)(3y) + (3y)2]

= (2x+ 3y) (8×2 – 6xy + 9y2)

a3 + b3 = (a+b)(a2 – ab + b2)

= a(a2 – ab + b2) + b(a2 – ab + b2)

= a3 – a2b + ab2 + a2b – ab2 + b3

= a3 – a2b + a2b + ab2 – ab2 + b3

= a3 – 0 + 0 + b3

= a3  + b3

Hence proved LHS = RHS

• There is another way to solve the expression as per the case given 

a3 + b3 =(a+b)3 – 3ab(a+b)

Example:-

a+ b = 5 and ab = 7

a3 + b3 = (a+b)3 -3ab(a + b)

        =  (5)3 – 3(7)(5)

    = 125 – 105

      = 20