Question: Method 2:
zero pair
10x - 4
Method 3:
Addition of polynomials can
be performed vertically by aligning
like terms.
+ 3x + 4
7x - 8
10x - 4
Place like terms under the same column and add.
Try it 1
Find the sum of $(5x^2 + 2x - 3) + (-2x^2 + 7)$.
Just for Fun
Insert the missing monomial
The missing monomial has
something to do with the
surrounding monomials in
combination.
17x
12x
-4x
7x
12x
28x
Example 2 Addition of Polynomials
Simplify $(3x^2y + 6xy + 8) + (2x^2y - 2xy - 11)$.
Solution:
By removing the parentheses and grouping like terms,
we get:
= $(3x^2y + 2x^2y) + (6xy - 2xy) + (8 - 11)$
= $(3 + 2)x^2y + (6 - 2)xy - 3$
= $5x^2y + 4xy - 3$
By aligning like terms vertically,
we get:
+ $3x^2y + 6xy + 8$
$2x^2y - 2xy - 11$
$5x^2y + 4xy - 3$
LET'S TALK
In which method in adding
polynomials is easier to use?
Discuss.
Try it 2
Simplify $(\frac{1}{4} x^2 - 2x + \frac{1}{3}) + (\frac{3}{4} x^2 - 7x - \frac{1}{12})$.
1. **State the problem:** Simplify the sum of the polynomials $$\left(\frac{1}{4} x^2 - 2x + \frac{1}{3}\right) + \left(\frac{3}{4} x^2 - 7x - \frac{1}{12}\right).$$
2. **Formula and rules:** To add polynomials, combine like terms by adding their coefficients.
3. **Group like terms:**
$$\left(\frac{1}{4} x^2 + \frac{3}{4} x^2\right) + (-2x - 7x) + \left(\frac{1}{3} - \frac{1}{12}\right)$$
4. **Add coefficients of like terms:**
- For $x^2$ terms: $$\frac{1}{4} + \frac{3}{4} = \frac{1+3}{4} = \frac{4}{4} = 1$$
- For $x$ terms: $$-2 - 7 = -9$$
- For constants: Find common denominator 12:
$$\frac{1}{3} = \frac{4}{12}$$
So,
$$\frac{4}{12} - \frac{1}{12} = \frac{3}{12} = \frac{1}{4}$$
5. **Write the simplified polynomial:**
$$1x^2 - 9x + \frac{1}{4}$$
6. **Final answer:**
$$x^2 - 9x + \frac{1}{4}$$
This is the sum of the given polynomials after combining like terms and simplifying fractions.