How to Use the Perfect Square Identity As a Shortcut in Expansion

Step-by-Step Guide

1. 1

   Step 1: Determine whether you have a perfect square binomial.

   A binomial is a two-termed expression.
   
   If the binomial expression is a perfect square, it will be expressed as either (a+b)2{\displaystyle (a+b)^{2}} or (a+b)(a+b){\displaystyle (a+b)(a+b)}.
   
   Note the binomials could also have a subtraction symbol.
   
   For example, (5y+3)2{\displaystyle (5y+3)^{2}} is a perfect square binomial.
2. 2

   Step 2: Set up the formula for a perfect square trinomial.

   The formula is (a+b)2=a2+2ab+b2{\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}}.
   
   If the binomials show subtraction, the formula is (a−b)2=a2−2ab+b2{\displaystyle (a-b)^{2}=a^{2}-2ab+b^{2}}.
   
   Note that a{\displaystyle a} is the first term of the binomial, and b{\displaystyle b} is the second term of the binomial. , This will become the first term of the trinomial.
   
   Remember that squaring a term means to multiply it by itself.
   
   For example, if you are expanding (5y+3)2{\displaystyle (5y+3)^{2}}, you would first calculate (5y)2=25y2{\displaystyle (5y)^{2}=25y^{2}}.
   
   So, 25y2{\displaystyle 25y^{2}} is the first term of the trinomial. , Make sure you are using the original a{\displaystyle a} and b{\displaystyle b} terms from the binomial expression.
   
   For example, if you are expanding (5y+3)2{\displaystyle (5y+3)^{2}}, you would calculate (5y)(3)=15y{\displaystyle (5y)(3)=15y}. , If the binomials show subtraction, you should multiply by
   -2.
   
   The result will be the middle term in the trinomial.
   
   For example, (2)(15y)=30y{\displaystyle (2)(15y)=30y}.
   
   So, your trinomial now looks like this: 25y2+30y+b2{\displaystyle 25y^{2}+30y+b^{2}}. , Again, make sure you are using the original b{\displaystyle b} term from the binomial expression.
   
   The square will give you the last term in the trinomial.For example, 32=9{\displaystyle 3^{2}=9}.
   
   So, (5y+3)2=25y2+30y+9{\displaystyle (5y+3)^{2}=25y^{2}+30y+9}
3. 3

   Step 3: Square the first term of the binomial.

4. 4

   Step 4: Multiply the first and last term.

5. 5

   Step 5: Multiply the product by 2.

6. 6

   Step 6: Square the last term.

Detailed Guide

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