Explanation:
To simplify expressions with polynomials, you need to combine like terms. Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms, and 2x² and 4x² are like terms. Constants (numbers without variables) are also like terms with each other.
When adding or subtracting polynomials, follow these steps:
1. Remove parentheses. Be careful with the minus sign in front of a parenthesis — it changes the sign of every term inside.
2. Group like terms together.
3. Add or subtract the coefficients of like terms.
Let’s solve each problem step by step.
1) (−5x + 4) + (3x − 2)
Remove parentheses: −5x + 4 + 3x − 2
Group like terms: (−5x + 3x) + (4 − 2)
Add: −2x + 2
2) (−6x² + 7x) − (7x² + 5x)
Remove parentheses (remember to distribute the minus): −6x² + 7x − 7x² − 5x
Group like terms: (−6x² − 7x²) + (7x − 5x)
Add: −13x² + 2x
3) (9x + 6) − (4x + 4)
Remove parentheses: 9x + 6 − 4x − 4
Group like terms: (9x − 4x) + (6 − 4)
Add: 5x + 2
4) (2x² + 7x) − (2x² + 3x)
Remove parentheses: 2x² + 7x − 2x² − 3x
Group like terms: (2x² − 2x²) + (7x − 3x)
Add: 0 + 4x = 4x
5) (7x² + 6x) + (3x² − 4x)
Remove parentheses: 7x² + 6x + 3x² − 4x
Group like terms: (7x² + 3x²) + (6x − 4x)
Add: 10x² + 2x
6) (−8x + 6) + (4x − 4)
Remove parentheses: −8x + 6 + 4x − 4
Group like terms: (−8x + 4x) + (6 − 4)
Add: −4x + 2
7) (6x² + 3x) + (4x² − 2x)
Remove parentheses: 6x² + 3x + 4x² − 2x
Group like terms: (6x² + 4x²) + (3x − 2x)
Add: 10x² + x
8) (9x² + 6x) − (7x² + 4x)
Remove parentheses: 9x² + 6x − 7x² − 4x
Group like terms: (9x² − 7x²) + (6x − 4x)
Add: 2x² + 2x
9) (5x² + 8x) + (3x² − 6x)
Remove parentheses: 5x² + 8x + 3x² − 6x
Group like terms: (5x² + 3x²) + (8x − 6x)
Add: 8x² + 2x
10) (−2x² + 7x) − (2x² + 5x)
Remove parentheses: −2x² + 7x − 2x² − 5x
Group like terms: (−2x² − 2x²) + (7x − 5x)
Add: −4x² + 2x
11) (−4x + 6) + (2x − 4)
Remove parentheses: −4x + 6 + 2x − 4
Group like terms: (−4x + 2x) + (6 − 4)
Add: −2x + 2
12) (−3x + 5) + (2x − 3)
Remove parentheses: −3x + 5 + 2x − 3
Group like terms: (−3x + 2x) + (5 − 3)
Add: −x + 2
13) (5x² + 9x) − (3x² + 7x)
Remove parentheses: 5x² + 9x − 3x² − 7x
Group like terms: (5x² − 3x²) + (9x − 7x)
Add: 2x² + 2x
Final Answer:
1) −2x + 2
2) −13x² + 2x
3) 5x + 2
4) 4x
5) 10x² + 2x
6) −4x + 2
7) 10x² + x
8) 2x² + 2x
9) 8x² + 2x
10) −4x² + 2x
11) −2x + 2
12) −x + 2
13) 2x² + 2x
Parent Tip: Review the logic above to help your child master the concept of addition and subtraction of polynomials worksheet.
