Table of Contents

**Algebraic Equation- For (a3 b3 Formula)**

An algebraic equation, often known as a polynomial equation, is a mathematical equation of the form:

**P = 0**

P is a polynomial having coefficients in a field, most commonly the field of rational numbers. Many authors solely use the word algebraic equation to describe univariate equations, or polynomial equations with only one variable. A polynomial equation, on the other hand, can have several variables. Polynomial equation is frequently favoured over algebraic equation when there are multiple variables (multivariate scenario).

**a**^{3} b^{3} Formula Proofs:

^{3}b

^{3}Formula Proofs:

- (a + b)
^{3}= a^{3}+ b^{3}+ 3ab (a + b) - (a – b)
^{3}= a^{3}– b^{3}– 3ab (a-b) - a
^{3}+ b^{3}= (a + b) (a^{2}– ab + b^{2}) - a
^{3}– b^{3}= (a – b) (a^{2}+ ab + b^{2}) - a
^{3}+ b^{3}+ c^{3}– 3abc = (a + b + c) (a^{2}+ b^{2}+ c^{2}– ab – bc – ca) - a + b = (a
^{3}+ b^{3}) / (a^{2}– ab + b^{2})

**a3 b3 Formula: Solutions And Examples**

**Problem: **Factorize 27x^{3} – 64y^{3}**Solution:** We can write 27x^{3} – 64y^{3} as (3x)^{3} – (4y)^{3}.

Therefore, by using the formula:

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

we get the factors as:

(3x – 4y) (9x^{2} + 16y^{2} + 12xy)

**Problem: **Factorize x^{3} + 8

**Solution: **The given equation x^{3} + 8 can be written as:

x^{3} + 2^{3}. therefore, it is of the form,

a^{3} + b^{3}.

Hence, by using the formula:

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

we get the factors as:

(x + 2) (x^{2} – x . 2 + 2^{2})

= (x + 2) ( x^{2} – 2x +4)

**Problem: **Find 8^{3} – 3^{3}**Solution:** By using the formula:

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

we get the solution as:

(5) × (8^{2} + 9 + 24) = 485

**Problem: **Factorize (2x + y)^{3} – (x + 2y)^{3}**Solution: **As this given equation is of the form a^{3} – b^{3},

Therefore, by using the formula:

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

we get the factors as:

(2x + y – x – 2y) [(2x + y)^{2} + (x + 2y)^{2} + (2x + y) (x + 2y)]

= (x – y) (7x^{2} + 7y^{2} + 13xy)

**Read More About:**

**a3 b3 Formula: FAQs**

**Ques: How do you prove a3 +b3?**

**Ans: **Proof: We take, **a3+b3+3ab(a+b)****=(a+b)2 (a+b)**

=> a3+b3 = (a+b)2 (a+b) – 3ab(a+b)

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

= (a+b)(a2+b2+2ab-3ab)

=> a3+b3 = (a+b)(a2+-ab+b2)

**Ques: What is this algebra?**

**Ans: **Algebra is a field of mathematics that aids in the depiction of problems and situations using mathematical expressions. To construct a meaningful mathematical statement, it uses variables like x, y, and z, as well as mathematical operations like addition, subtraction, multiplication, and division.

**Ques: What is the Algebra formula?**

**Ans: **Algebra Formulas: What Are They? An algebraic formula is a mathematical or algebraic rule represented as an equation. It’s a two-sided equation with algebraic expressions on both sides. The algebraic formula is a quick and easy way to answer difficult algebraic problems.