7.2 Adding and Subtracting Polynomials

We will look at 3 different ways to add polynomials:

1. Using algebra tiles2. Horizontal method3. Vertical method

Methods for Adding

Group like terms and simplify.Example:(-x2 + 5x + 4) + (3x2 – 8x + 9)

Horizontal Method

Line up like terms vertically, then add.Leave a space for any missing terms.Example:(3a2 + 8) + (5a – 1)

Vertical Method

Find the sum:(b – 10) + (4b – 3)

(x2 – x – 2) + (7x2 – x)

You Try!

Just add the opposite!Change all the signs of the subtracted polynomial

Then add like termsExample:(y2 + 4y + 2) – (2y2 – 5y – 3)

Subtracting Polynomials

Find the difference:(5x2 + 4x – 1) – (2x2 – 6)

Example:

Find the difference:(p2 + p + 3) – (-4p2 – p + 3)

(-k + 5) – (3k2 – 6)

You Try!

Just like one-variable, but be EXTRA careful grouping like terms.

Example:(x2 – 2xy – y2) + (x2 + xy + y2)

Adding/Subtracting Multi-Variable Polynomials

(2s2 – 5st – t2) – (s2 + 7st – t2)

Example:

(c2 – 6d2) + (c2 – 2cd + 2d2)

Example:

(-x2 + 9xy) – (x2 + 6xy – 8y2)

(a2 – 3ab + 2b2) + (-4a2 + 5ab – b2)

You Try!