Expanding polynomials
Expand & simplify: (x + 1)(x + 2 + 3)
x2 + 6x + 5
Perform FOIL on : (x + 1)(x + 2)
x2 + 3x + 2
In an expression, the parts being added together or subtracted. Example: 4x + 3x + 3y + 7y
A term
3e + 8e - 4e
7e
What does the acronym "FOIL" stand for?
First, Outside, Inside, Last
Expand & simplify: (x - 2)(x + 5 - 3)
x2 - 4
Perform FOIL on: (x - 3)(x + 4)
x2 + x - 12
A word for an algebraic expression that involves subtracting or adding exactly two terms. Example: 2x - 3y
Binomial
100w - 5s + 30w
130w - 5s
True or False: 4x2y is equivalent to 4yx2
True
Expand & Simplify : (w2 - w)(x + 5 + 2w)
2w3 + 3w2 + w2x - wx - 5w
Perform FOIL on: (2y + 3)(3y - 7)
6y2 - 5y - 21
A rule that allows the addition of exponents when multiplying the same variable term together. Example: (x2)(x3) = x5
Product Rule
-6y - 3xy + 4x - 5x + 4y
-2y - 3xy - x
True or False: (x - 2 + 6)(x2 + 5x - 2) is equivalent to (x + 4)(x2 + 5x - 2).
True
Expand & Simplify: (x - 3 + 5)(2x + 3 + 4x2)
4x3 + 10x2 + 7x + 6
Perform FOIL on: (2xy + y)(3x + xy)
2x2y2 + 6x2y + xy2 + 3xy
Terms that contain the same variable(s) raised to the same exponent. These terms can be combined. Example: 3x + 9x or 7y + 3Y
Like Terms
5x + 6xy + 4x2 + 10xy + 11y + 5y
4x2 + 5x + 16xy + 16y
True or False: A polynomial contains exactly 3 terms.
False, a polynomial contains 3 or more terms.
Expand & Simplify : (2x - x2 + 4)(x3 + 4x - 6)
-x5 + 2x4 + 14x2 + 4x - 24
Perform FOIL on: (-4xy + 5)(8y + 7x)
-32xy2 - 28x2y + 40y + 35x
To perform all indicated operations, including combining like terms. When you do this you do not always get a number answer like 25 or 10 or -1. Frequently you get an expression as an answer, like 2x + 5.
Simplify
5yx + 4w + 3y + 7x2 - 10w + 3x + 12w - 3xy + 5x2
12x2 + 2xy + 3x + 3y + 6w
Expand and simplify: x2 + (x2 - 3)2 + 6x - 3y + 4xy + 7y
x4 - 5x2 + 6x + 4y + 4xy + 9