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# How do I expand quadratics?

By Lee Mansfield on the 11th of June, 2012

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# Expand & Factorize Quadratic Expressions

Quadratic expressions are algebraic expressions where the variable has a power of 2.

For example: x2+3x+4

To expand quadratic equations, use the FOIL (First, Outside, Inside, Last) method.

First Outside Inside Last

## Example 1

Expand (x+3)(x+2)

(x+3)(x+2)=x(x+2)+3(x+2)=x2+2x+3x+6=x2+5x+6

(x+3)(x+2)=x2+2x+3x+6=x2+5x+6

## Example 2

(x+4)(x2)=x22x+4x8=x2+2x8

## Example 3

(2x+5)(3x8)=6x216x+15x40=6x2x40

## Questions - Expand Using FOIL

Q1. (x+6)(x+5)
Q2. (x5)(x4)
Q3. (2x+5)(6x2)

A1. x2+11x+30
A2. x29x+20
A3. 12x2+26x10

## Perfect Squares

(x+a)2=x2+2ax+a2(xa)2=x22ax+a2

## Example 4

(x+5)2=(x+5)(x+5)=x2+10x+25

## Example 5

(x3)2=(x3)(x3)=x26x+9

## Questions - Expand These Perfect Squares

Q1. (x+7)2
Q2. (2x+5)2

A1. x2+14x+49
A2. 4x2+20x+25

## Difference of Squares

(x+a)(xa)=x2a2

## Example 6

(x+5)(x5)=x25x+5x25=x225

## Example 7

(x3)(x+3)=x23x+3x9=x29

## Questions - Expand These Difference of Squares

Q1. (x+7)(x7)
Q2. (2x+5)(2x5)

A1. x249
A2. 4x225

Factorizing is the reverse of expanding.

## Example 8

x2+6x+5=(x+5)(x+1)

## Example 9

6x2+2x20=(2x+4)(3x5)

## Questions - Factorize

Q1. x27x8
Q2. x2+x12

A1. (x8)(x+1)
A2. (x+4)(x3)

By kristen k on the 17th of January, 2013