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} = a^{2} + 2ab + b^{2}
(a – b)^{2} = a^{2} – 2ab + b^{2}
a^{2} – b^{2} = (a – b)(a + b)
a^{2} + b^{2} = (a – b)^{2} + 2ab = (a + b)^{2} – 2ab
(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2ac + 2bc
(a – b – c)^{2} = a^{2} + b^{2} + c^{2} – 2ab – 2ac + 2bc
(a + b + c + …)^{2} = a^{2} + b^{2} + c^{2} + … + 2(ab + ac + bc + …..)

Cube based formula:
(a + b)^{3} = a^{3} + b^{3} + 3ab(a + b) ; (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}
(a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}
a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})
a^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2})
(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}
(a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}

4^{th} power algebra formula:
(a + b)^{4} = a^{4} + 4a^{3}b + 6a^{2}b^{2} + 4ab^{3} + b^{4})
(a – b)^{4} = a^{4} – 4a^{3}b + 6a^{2}b^{2} – 4ab^{3} + b^{4})
a^{4} – b^{4} = (a – b)(a + b)(a^{2} + b^{2})

5^{th} power formula:
a^{5} – b^{5} = (a – b)(a^{4} + a^{3}b + a^{2}b^{2} + ab^{3} + b^{4})

nth power algebra formula
If n is a natural number, a^{n} – b^{n} = (a – b)(a^{n1} + a^{n2}b+.…+ b^{n2}a + b^{n1})
If n is even (n = 2k), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +….+ b^{n2}a – b^{n1})
If n is odd (n = 2k + 1), a^{n} + b^{n} = (a + b)(a^{n1} – a^{n2}b +…. b^{n2}a + b^{n1})
(a + b + c + …)^{2} = a^{2} + b^{2} + c^{2} + … + 2(ab + ac + bc + …..)

Laws of Exponents (algebra formula)
(p^{m})(p^{n}) = p^{m+n}
(pq)^{m} = p^{m}q^{m}
(p^{m})^{n} = p^{mn}

Fractional exponents:
$$a^{0}={1}$$
$$\frac{a^{m}}{a^{n}} = a^{mn}{(if m>n)}$$
$$={1 (if m=n)}$$
$$=\frac{1}{a^{nm}} {(if m<n)}$$
$$p^{m}= \frac{1}{a^{m}}$$
$$a^{m}=\frac{1}{a^{m}}$$

Solved examples on algebra formula:
Q. Sove the question 15^{2}5^{2}.
Solution:
As, a^{2} – b^{2} = (a – b)(a + b)
So,
15^{2}5^{2 }= (155)(15+5)
= (10)(20)
=200
Q. Sove the question 5^{2 }x 5^{4}.
By using exponential equation (p^{m})(p^{n}) = p^{m+n}
so, 5^{2}x5^{4 }= 5^{6} = 78125
Q.Find the square of 4x+y.
As, (a + b)^{2} = a^{2} + 2ab + b^{2}
(4x+y)^{2}= (4x)^{2 }+ 2(4xy) + (y)^{2}
= 16x^{2}+ 8xy + y^{2}
Q.Express 16x^{2}+24xy +9y^{2 }as a perfect square.
Solution:
16x^{2}+20xy +16y^{2}
=(4x)^{2}+ 2.4x.3y + (3y)^{2}
= (4x + 3y)^{2}
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