# Algebra Formula:

Do you ever think that if algebra were not there then how the mathematics would be? It would be like a human without a heart. Some of you think that it must be quiet interesting as we dont had to learn the algebra formula (jokes apart). For them, we have made it easy learning the formulas. In mathematics, algebra formula has a great use every time. we have made a list and PDF of algebra formula to ensure you better with the algebraic section.

Each formula which you need in solving Algebraic equation is listed here. Algebra formulas list for class 8, 9, 10, 11 & 12 will also help you in all competitive examinations like SSC, Railway, CBSE board etc. You must know that basic algebraic identities is in CBSE class 8 syllabus. Take a look at the algebra formula list below:

• ## Square algebra formula

(a + b)2 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

a2 – b2 = (a – b)(a + b)

a2 + b2 = (a – b)2 + 2ab = (a + b)2 – 2ab

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc

(a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc

(a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + …..)

• ## Cube based formula:

(a + b)3 = a3 + b3 + 3ab(a + b) ; (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)3 = a3 + 3a2b + 3ab2 + b3

(a – b)3 = a3 – 3a2b + 3ab2 – b3

(a + b + c)

• ## 4th power algebra formula:

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)

(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)

a4 – b4 = (a – b)(a + b)(a2 + b2)

• ## 5th power formula:

a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)

• ## nth power algebra formula

If n is a natural number, an – bn = (a – b)(an-1 + an-2b+.…+ bn-2a + bn-1)

If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +….+ bn-2a – bn-1)

If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +….- bn-2a + bn-1)

(a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + …..)

(pm)(pn) = pm+n

(pq)m = pmqm

(pm)n = pmn

• ## Fractional exponents:

$$a^{0}={1}$$

$$\frac{a^{m}}{a^{n}} = a^{m-n}{(if m>n)}$$

$$={1 (if m=n)}$$

$$=\frac{1}{a^{n-m}} {(if m<n)}$$

$$p^{m}= \frac{1}{a^{-m}}$$

$$a^{-m}=\frac{1}{a^{m}}$$

Those who want to solve questions then they can download algebra formula in pdf format. You can download it and learn it easily whenever & wherever you want.

Algebra formula PDF Chart is available here to download. From the link provided below you can download Algebraic formula, equations pdf. The light pdf here includes all the formula from class 6 to class 12th. Take a look at it.

• ## Solved examples on algebra formula:

### Q. Sove the question 152-52.

Solution:

As, a2 – b2 = (a – b)(a + b)

So,
152-52 = (15-5)(15+5)
= (10)(20)
=200

### Q. Sove the question 52 x 54.

By using exponential equation (pm)(pn) = pm+n
so, 52x5= 56 = 78125

### Q.Find the square of 4x+y.

As, (a + b)2 = a2 + 2ab + b2
(4x+y)2= (4x)2 + 2(4xy) + (y)2
= 16x2+ 8xy + y2

### Q.Express 16x2+24xy +9y2 as a perfect square.

Solution:

16x2+20xy +16y2
=(4x)2+ 2.4x.3y + (3y)2
= (4x + 3y)2