Question

kuta software - infinite algebra 1
name:
adding and subtracting polynomials
date____ period __
simplify each expression.

1. $(5p^{2}-3)+(2p^{2}-3p^{3})$
2. $(a^{3}-2a^{2})-(3a^{2}-4a^{3})$
3. $(4+2n^{3})+(5n^{3}+2)$
4. $(4n-3n^{3})-(3n^{3}+4n)$
5. $(3a^{2}+1)-(4+2a^{2})$
6. $(4r^{3}+3r^{4})-(r^{4}-5r^{3})$
7. $(5a+4)-(5a+3)$
8. $(3x^{4}-3x)-(3x-3x^{4})$
9. $(-4k^{4}+14+3k^{2})+(-3k^{4}-14k^{2}-8)$
10. $(3-6n^{5}-8n^{4})-(-6n^{4}-3n-8n^{5})$
11. $(12a^{5}-6a-10a^{3})-(10a-2a^{5}-14a^{4})$
12. $(8n-3n^{4}+10n^{2})-(3n^{2}+11n^{4}-7)$
13. $(-x^{4}+13x^{5}+6x^{3})+(6x^{3}+5x^{5}+7x^{4})$
14. $(9r^{3}+5r^{2}+11r)+(-2r^{3}+9r-8r^{2})$
15. $(13n^{2}+11n-2n^{4})+(-13n^{2}-3n-6n^{4})$
16. $(-7x^{5}+14-2x)+(10x^{4}+7x+5x^{5})$

Explanation:

Step1: Combine like terms

$(5p^2 - 3) + (2p^2 - 3p^2) = 5p^2 + 2p^2 - 3p^2 - 3$

Step2: Calculate coefficients

$=(5+2-3)p^2 - 3 = 4p^2 - 3$

Step1: Distribute negative sign

$(a^3 - 2a^2) - (3a^2 - 4a^3) = a^3 - 2a^2 - 3a^2 + 4a^3$

Step2: Combine like terms

$=(1+4)a^3 + (-2-3)a^2 = 5a^3 - 5a^2$

Step1: Combine like terms

$(4 + 2n^2) + (5n^2 + 2) = 2n^2 + 5n^2 + 4 + 2$

Step2: Calculate sums

$=(2+5)n^2 + (4+2) = 7n^2 + 6$

Step1: Distribute negative sign

$(4n - 3n^3) - (3n^2 + 4n) = 4n - 3n^3 - 3n^2 - 4n$

Step2: Combine like terms

$=-3n^3 - 3n^2 + (4-4)n = -3n^3 - 3n^2$

Step1: Distribute negative sign

$(3a^2 + 1) - (4 + 2a^2) = 3a^2 + 1 - 4 - 2a^2$

Step2: Combine like terms

$=(3-2)a^2 + (1-4) = a^2 - 3$

Step1: Distribute negative sign

$(4r^3 + 3r^4) - (r^4 - 5r^3) = 4r^3 + 3r^4 - r^4 + 5r^3$

Step2: Combine like terms

$=(3-1)r^4 + (4+5)r^3 = 2r^4 + 9r^3$

Step1: Distribute negative sign

$(5a + 4) - (5a + 3) = 5a + 4 - 5a - 3$

Step2: Combine like terms

$=(5-5)a + (4-3) = 1$

Step1: Distribute negative sign

$(3x^4 - 3x) - (3x - 3x^4) = 3x^4 - 3x - 3x + 3x^4$

Step2: Combine like terms

$=(3+3)x^4 + (-3-3)x = 6x^4 - 6x$

Step1: Combine like terms

$(-4k^4 + 14 + 3k^2) + (-3k^4 - 14k^2 - 8) = -4k^4 - 3k^4 + 3k^2 - 14k^2 + 14 - 8$

Step2: Calculate sums

$=(-4-3)k^4 + (3-14)k^2 + (14-8) = -7k^4 - 11k^2 + 6$

Step1: Distribute negative sign

$(3 - 6n^5 - 8n^4) - (-6n^4 - 3n - 8n^5) = 3 - 6n^5 - 8n^4 + 6n^4 + 3n + 8n^5$

Step2: Combine like terms

$=(-6+8)n^5 + (-8+6)n^4 + 3n + 3 = 2n^5 - 2n^4 + 3n + 3$

Step1: Distribute negative sign

$(12a^5 - 6a - 10a^3) - (10a - 2a^5 - 14a^4) = 12a^5 - 6a - 10a^3 - 10a + 2a^5 + 14a^4$

Step2: Combine like terms

$=(12+2)a^5 + 14a^4 - 10a^3 + (-6-10)a = 14a^5 + 14a^4 - 10a^3 - 16a$

Step1: Distribute negative sign

$(8n - 3n^4 + 10n^2) - (3n^2 + 11n^4 - 7) = 8n - 3n^4 + 10n^2 - 3n^2 - 11n^4 + 7$

Step2: Combine like terms

$=(-3-11)n^4 + (10-3)n^2 + 8n + 7 = -14n^4 + 7n^2 + 8n + 7$

Step1: Combine like terms

$(-x^4 + 13x^5 + 6x^3) + (6x^3 + 5x^5 + 7x^4) = 13x^5 + 5x^5 + (-x^4 + 7x^4) + 6x^3 + 6x^3$

Step2: Calculate sums

$=(13+5)x^5 + (-1+7)x^4 + (6+6)x^3 = 18x^5 + 6x^4 + 12x^3$

Step1: Combine like terms

$(9r^3 + 5r^2 + 11r) + (-2r^3 + 9r - 8r^2) = 9r^3 - 2r^3 + 5r^2 - 8r^2 + 11r + 9r$

Step2: Calculate sums

$=(9-2)r^3 + (5-8)r^2 + (11+9)r = 7r^3 - 3r^2 + 20r$

Step1: Combine like terms

$(13n^2 + 11n - 2n^4) + (-13n^2 - 3n - 6n^4) = -2n^4 - 6n^4 + 13n^2 - 13n^2 + 11n - 3n$

Step2: Calculate sums

$=(-2-6)n^4 + (13-13)n^2 + (11-3)n = -8n^4 + 8n$

Step1: Combine like terms

$(-7x^5 + 14 - 2x) + (10x^4 + 7x + 5x^5) = -7x^5 + 5x^5 + 10x^4 - 2x + 7x + 14$

Step2: Calculate sums

$=(-7+5)x^5 + 10x^4 + (-2+7)x + 14 = -2x^5 + 10x^4 + 5x + 14$

Answer:

1. $4p^2 - 3$
2. $5a^3 - 5a^2$
3. $7n^2 + 6$
4. $-3n^3 - 3n^2$
5. $a^2 - 3$
6. $2r^4 + 9r^3$
7. $1$
8. $6x^4 - 6x$
9. $-7k^4 - 11k^2 + 6$
10. $2n^5 - 2n^4 + 3n + 3$
11. $14a^5 + 14a^4 - 10a^3 - 16a$
12. $-14n^4 + 7n^2 + 8n + 7$
13. $18x^5 + 6x^4 + 12x^3$
14. $7r^3 - 3r^2 + 20r$
15. $-8n^4 + 8n$
16. $-2x^5 + 10x^4 + 5x + 14$