Quadratic Expressions

Monomial Common Factors

Both x and y are being
multiplied by 3, making it
able to be factored out.

3y+3x
=3(x+y)

Binomial Common Factors

x-3 is multiplied by both 2 and 3y,
making it able to factor out.

2(x-3)+3y(x-3)
=(x-3)(2+3y)

Group Common Factors

Group both sides so to
factor them separately

X^4-2x^3 + 4x-8

A=1

(1)x^2+bx+c
=(x+1)(x+c)

A=/=1

ax+bx+c

_+_=b

_ * _=ac

Perfect Square Trinomials

A^2+2AB+B^2
=(A+B)(A+B)

A^2-2AB+B^2
=(A-B)(A-B)

Difference of Squares

square root both
terms and have a
square outside the
bracket to show it
was factored, expand
both terms, and follow
binomial common factor.

36y^2-100
=(6y)^2-(10)^2
=(6y)(6y)-(10)(10)
=(6y-10)(6y+10)

Distributive property

Multiply everything inside the
brackets by the number(s) outside of it.

3(2x+4)
=6x+12

Multiplying Binomials

Follow FOIL method.

(2x+4)(3x+2)
=6x^2+12x+6

Squaring binomials

Expand, then follow foil method.

(a+b)^2
=(a+b)(a+b)
=a^2+2ab+b^2

Difference of squares

Follow FOIL method
and remember to cancel
out reciprocals.

(a-b)(a+b)
=A^2+ab-ab+B^2
=A^2+B^2