Algebra Formulas

Algebra is a fundamental branch of mathematics that deals with the manipulation of variables and equations. Mastering algebra formulas is crucial for solving a wide range of mathematical problems, from simple linear equations to complex systems of equations. Here are some of the most important algebra formulas you should know:

Algebra Formulas

ALGEBRA FORMULAS

Arithmetic Properties

( a + b ) 2 = a 2 + 2 a b + b 2 ( a b ) 2 = a 2 2 a b + b 2 a 2 + b 2 = ( a + b ) 2 2 a b a 2 b 2 = ( a + b ) ( a b ) ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 a b + 2 b c + 2 c a ( a + b c ) 2 = a 2 + b 2 + c 2 + 2 a b 2 b c 2 c a ( a b c ) 2 = a 2 + b 2 + c 2 2 a b + 2 b c 2 c a ( a + b ) 3 = a 3 + 3 a 2 b + 3 a b 2 + b 3 = a 3 + b 3 + 3 a b ( a + b ) ( a b ) 3 = a 3 3 a 2 b + 3 a b 2 b 3 = a 3 b 3 3 a b ( a b ) a 3 b 3 = ( a b ) ( a 2 + a b + b 2 ) a 3 + b 3 = ( a + b ) ( a 2 a b + b 2 ) ( a + b ) 4 = a 4 + 4 a 3 b + 6 a 2 b 2 + 4 a b 3 + b 4 ( a b ) 4 = a 4 4 a 3 b + 6 a 2 b 2 4 a b 3 + b 4 a 4 b 4 = ( a + b ) ( a b ) ( a 2 + b 2 ) a 5 b 5 = ( a b ) ( a 4 + a 3 b + a 2 b 2 + a b 3 + b 4 ) ( a + b ) 2 = a 2 + 2 a b + b 2 ( a b ) 2 = a 2 2 a b + b 2 a 2 + b 2 = ( a + b ) 2 2 a b a 2 b 2 = ( a + b ) ( a b ) ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 a b + 2 b c + 2 c a ( a + b c ) 2 = a 2 + b 2 + c 2 + 2 a b 2 b c 2 c a ( a b c ) 2 = a 2 + b 2 + c 2 2 a b + 2 b c 2 c a ( a + b ) 3 = a 3 + 3 a 2 b + 3 a b 2 + b 3 = a 3 + b 3 + 3 a b ( a + b ) ( a b ) 3 = a 3 3 a 2 b + 3 a b 2 b 3 = a 3 b 3 3 a b ( a b ) a 3 b 3 = ( a b ) a 2 + a b + b 2 a 3 + b 3 = ( a + b ) a 2 a b + b 2 ( a + b ) 4 = a 4 + 4 a 3 b + 6 a 2 b 2 + 4 a b 3 + b 4 ( a b ) 4 = a 4 4 a 3 b + 6 a 2 b 2 4 a b 3 + b 4 a 4 b 4 = ( a + b ) ( a b ) a 2 + b 2 a 5 b 5 = ( a b ) a 4 + a 3 b + a 2 b 2 + a b 3 + b 4 {:[(a+b)^(2)=a^(2)+2ab+b^(2)],[(a-b)^(2)=a^(2)-2ab+b^(2)],[a^(2)+b^(2)=(a+b)^(2)-2ab],[a^(2)-b^(2)=(a+b)(a-b)],[(a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca],[(a+b-c)^(2)=a^(2)+b^(2)+c^(2)+2ab-2bc-2ca],[(a-b-c)^(2)=a^(2)+b^(2)+c^(2)-2ab+2bc-2ca],[(a+b)^(3)=a^(3)+3a^(2)b+3ab^(2)+b^(3)],[quad=a^(3)+b^(3)+3ab(a+b)],[(a-b)^(3)=a^(3)-3a^(2)b+3ab^(2)-b^(3)],[quad=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+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))],[a^(5)-b^(5)=(a-b)(a^(4)+a^(3)b+a^(2)b^(2)+ab^(3)+b^(4))]:}\begin{aligned} & (a+b)^{2}=a^{2}+2 a b+b^{2} \\ & (a-b)^{2}=a^{2}-2 a b+b^{2} \\ & a^{2}+b^{2}=(a+b)^{2}-2 a b \\ & a^{2}-b^{2}=(a+b)(a-b) \\ & (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a \\ & (a+b-c)^{2}=a^{2}+b^{2}+c^{2}+2 a b-2 b c-2 c a \\ & (a-b-c)^{2}=a^{2}+b^{2}+c^{2}-2 a b+2 b c-2 c a \\ & (a+b)^{3}=a^{3}+3 a^{2} b+3 a b^{2}+b^{3} \\ & \quad=a^{3}+b^{3}+3 a b(a+b) \\ & (a-b)^{3}=a^{3}-3 a^{2} b+3 a b^{2}-b^{3} \\ & \quad=a^{3}-b^{3}-3 a b(a-b) \\ & a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right) \\ & a^{3}+b^{3}=(a+b)\left(a^{2}-a b+b^{2}\right) \\ & (a+b)^{4}=a^{4}+4 a^{3} b+6 a^{2} b^{2}+4 a b^{3}+b^{4} \\ & (a-b)^{4}=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4} \\ & a^{4}-b^{4}=(a+b)(a-b)\left(a^{2}+b^{2}\right) \\ & a^{5}-b^{5}=(a-b)\left(a^{4}+a^{3} b+a^{2} b^{2}+a b^{3}+b^{4}\right) \end{aligned}