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Algebra formula

algebraic formula

Also, read
Introduction to Algebra
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Algebraic Formula for Class 12

Algebra Formula:

In mathematics, algebra formula has a great use every time. we have made a list of formula to ensure you better with the algebraic section.

Each formula which you need in solving Algebraic equation is listed here.

  • Square based 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

  • 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 + …..)

  • Laws of Exponents (algebra formula)

(pm)(pn) = pm+n

(pq)m = pmqm

(pm)n = pmn

  • Fractional exponents:

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

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

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

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

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

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

  • 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 5x 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

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