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Here are a few recommended readings before getting started with this lesson.
When a binomial is squared, the resulting expression is a perfect square trinomial.
(a+b)2=a2+2ab+b2(a−b)2=a2−2ab+b2
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
Calculate the area of a square with side lengths x+2 feet. Then, calculate the area of a square with side lengths x−1 feet. Finally, find the difference between these areas.
(a+b)2=a2+2ab+b2
Commutative Property of Multiplication
Calculate power
Multiply
The area of a square is calculated by squaring its side length.
(a+b)2=a2+2ab+b2
(ab)m=ambm
(am)n=am⋅n
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
The area of a square is calculated by squaring its side length. The area of a rectangle is calculated by multiplying the length by the width.
(a+b)2=a2+2ab+b2
(ab)m=ambm
(am)n=am⋅n
Multiply
am⋅an=am+n
(a−b)2=a2−2ab+b2
(am)n=am⋅n
Commutative Property of Multiplication
Multiply
a⋅am=a1+m
(ab)m=ambm
Identity Property of Multiplication
(a+b)(a−b)=a2−b2
(ab)m=ambm
(am)n=am⋅n
1a=1
State the degree and the leading coefficient of the resulting polynomial after squaring the binomial or multiplying the conjugate binomials.
LHS⋅(a+b)=RHS⋅(a+b)
Commutative Property of Multiplication
a⋅am=a1+m