When a binomial is squared, the resulting expression is a perfect square trinomial.
For simplicity, depending on the sign of the binomial, these two identities can be expressed as one.
(a±b)2=a2±2ab+b2
This rule will be first proven for (a+b)2 and then for (a−b)2.
a2=a⋅a
Distribute (a+b)
Distribute a
Distribute b
Commutative Property of Multiplication
Add terms
a2=a⋅a
Distribute (a−b)
Distribute a
Distribute -b
Commutative Property of Multiplication
Subtract terms
Rewrite (x+3)2 and (7−x)2 as perfect square trinomials.
(a+b)2=a2+2ab+b2
Multiply
Calculate power
(a−b)2=a2−2ab+b2
Calculate power
Multiply
The product of two conjugate binomials is the difference of two squares.
(a+b)(a−b)=a2−b2
Distribute (a−b)
Distribute a
Distribute b
Commutative Property of Multiplication
Add terms
Multiply parentheses
Multiply
Commutative Property of Addition
Simplify terms
Multiply parentheses
Multiply
Commutative Property of Addition
Simplify terms
Find all complex solutions to the equation x3−43=0 by using the difference of two cubes.
Commutative Property of Multiplication
Calculate power
Use the Quadratic Formula: a=1,b=4,c=16
Calculate power and product
Subtract term
-a=ia
State solutions
Split into factors
a⋅b=a⋅b
Calculate root
Simplify quotient
(a−b)2=a2−2ab+b2
(a⋅b)m=am⋅bm
Calculate power
Commutative Property of Addition
Simplify terms