Download all the basic algebra formulas in pdf for the offline practising and learning. All the listed formulas are very important. We should not miss leaning any formula.

To learn the formulas each and every time we can’t search online, so downloading in pdf all the algebra formulas is the best option. Wherever and whenever you want you can check the formulas for the reference. If you want proof for the formulas, for some formulas I have given check it.

## List of complete algebra formulas as follows:

Below I have given all the formulas in algebra which are useful. If you want you can download all these algebra formulas in pdf.

• ${ \left( a+b \right) }^{ 2 }$ = ${ a }^{ 2 }$ + 2ab + ${ b }^{ 2 }$ (proof of a+b whole square formula)
• ${ a }^{ 2 }$ + ${ b }^{ 2 }$ = ${ \left( a+b \right) }^{ 2 }$ – 2ab  (from above formula we get this)
• ${ \left( a+b+c \right) }^{ 2 }$  = ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ + 2ab + 2bc + 2ca (proof of a+b+c whole square formula) or

= ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ + 2 (ab + bc + ca) (taking 2 common)

• ${ \left( -a+b+c \right) }^{ 2 }$  = ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ – 2ab + 2bc – 2ca  or

= ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ + 2 (-ab + bc -ca) (taking 2 common)

• ${ \left( a-b+c \right) }^{ 2 }$  = ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ – 2ab -2bc + 2ca  or

= ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ + 2 (-ab – bc + ca) (taking 2 common)

• ${ \left( a+b-c \right) }^{ 2 }$  = ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ + 2ab – 2bc – 2ca or

= ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ + 2 (ab – bc – ca) (taking 2 common)

• ${ \left( -a-b-c \right) }^{ 2 }$  = ${ \left( a+b+c \right) }^{ 2 }$ = ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ + 2ab + 2bc + 2ca  (both are same)
• ${ \left( a-b \right) }^{ 2 }$ = ${ a }^{ 2 }$ – 2ab + ${ b }^{ 2 }$   (in ${ \left( a+b \right) }^{ 2 }$ formula, replace + sign with – sign)
• ${ a }^{ 2 }$ + ${ b }^{ 2 }$ = ${ \left( a-b \right) }^{ 2 }$ + 2ab   (from above formula we get this)
• (a+b) (a-b) = ${ a }^{ 2 }$${ b }^{ 2 }$ (proof of a square minus b square formula)
• ${ \left( a+b \right) }^{ 2 }$ + ${ \left( a-b \right) }^{ 2 }$ = 2${ a }^{ 2 }$ + 2${ b }^{ 2 }$ = 2 (${ a }^{ 2 }$ + ${ b }^{ 2 }$)
• ${ \left( a+b \right) }^{ 2 }$${ \left( a-b \right) }^{ 2 }$ = 4ab  (on simplifying both formulas )
• ${ \left( a+b \right) }^{ 3 }$ ${ a }^{ 3 }$ + 3${ a }^{ 2 }$b + 3a${ b }^{ 2 }$ + ${ b }^{ 3 }$ (proof of a plus b whole cube formula)

= ${ a }^{ 3 }$ + ${ b }^{ 3 }$ + 3ab (a+b)

• ${ \left( a-b \right) }^{ 3 }$${ a }^{ 3 }$ – 3${ a }^{ 2 }$b + 3a${ b }^{ 2 }$${ b }^{ 3 }$ (proof of a minus b whole cube formula)

= ${ a }^{ 3 }$${ b }^{ 3 }$ – 3ab (a-b) (by taking common terms)

• ${ a }^{ 3 }$${ b }^{ 3 }$ = (a-b) (${ a }^{ 2 }$ + ab + ${ b }^{ 2 }$) (from above formula we get this)
• ${ a }^{ 3 }$ + ${ b }^{ 3 }$ = (a+b) (${ a }^{ 2 }$ – ab + ${ b }^{ 2 }$) (proof of a cube plus b cube formula)
• (x+a) (x+b) = ${ x }^{ 2 }$ + (a+b)x + ab  (general formula)
• (x+a) (x+b) (x+c) = ${ x }^{ 3 }$ + (a+b+c) ${ x }^{ 2 }$ + (ab+bc+ca) x + abc (useful while solving problems)
• (a+b+c) (${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ –ab-bc-ca) = ${ a }^{ 3 }$ +${ b }^{ 3 }$ +${ c }^{ 3 }$ -3abc  (one of the useful formula in competitive exams)