Question

add and subtract the polynomials (make sure to combine like terms and watch your signs!);
$(5p^3 - 3)+(2p^3 - 3p^3)$
$(a^3 - 2a^2)-(3a^2 - 4a^3)$

$(4 + 2n^3)+(5n^3 + 2)$
$(4n - 3n^3)-(3n^3 + 4n)$

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

$(5a + 4)-(5a + 3)$
$(3x^4 - 3x)-(3x - 3x^4)$

$(-4k^4 + 14 + 3k^2)+(-3k^4 - 14k^2 - 8)$
$(3 - 6n^5 - 8n^4)-(-6n^4 - 3n$

Explanation:

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Problem 1: $(5p^3 - 3) + (2p^3 - 3p^3)$

Step1: Remove parentheses

$5p^3 - 3 + 2p^3 - 3p^3$

Step2: Combine like terms

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

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Problem 2: $(a^3 - 2a^2) - (3a^2 - 4a^3)$

Step1: Distribute the negative sign

$a^3 - 2a^2 - 3a^2 + 4a^3$

Step2: Combine like terms

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

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Problem 3: $(4 + 2n^3) + (5n^3 + 2)$

Step1: Remove parentheses

$4 + 2n^3 + 5n^3 + 2$

Step2: Combine like terms

$(2n^3+5n^3)+(4+2) = 7n^3 + 6$

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Problem 4: $(4n - 3n^3) - (3n^3 + 4n)$

Step1: Distribute the negative sign

$4n - 3n^3 - 3n^3 - 4n$

Step2: Combine like terms

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

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

Step1: Distribute the negative sign

$3a^2 + 1 - 4 - 2a^2$

Step2: Combine like terms

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

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Problem 6: $(4r^3 + 3r^4) - (r^4 - 5r^3)$

Step1: Distribute the negative sign

$4r^3 + 3r^4 - r^4 + 5r^3$

Step2: Combine like terms

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

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Problem 7: $(5a + 4) - (5a + 3)$

Step1: Distribute the negative sign

$5a + 4 - 5a - 3$

Step2: Combine like terms

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

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Problem 8: $(3x^4 - 3x) - (3x - 3x^4)$

Step1: Distribute the negative sign

$3x^4 - 3x - 3x + 3x^4$

Step2: Combine like terms

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

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Problem 9: $(-4k^4 + 14 + 3k^2) + (-3k^4 - 14k^2 - 8)$

Step1: Remove parentheses

$-4k^4 + 14 + 3k^2 - 3k^4 - 14k^2 - 8$

Step2: Combine like terms

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

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Problem 10: $(3 - 6n^5 - 8n^4) - (-6n^4 - 3n)$

Step1: Distribute the negative sign

$3 - 6n^5 - 8n^4 + 6n^4 + 3n$

Step2: Combine like terms

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

Answer:

1. $4p^3 - 3$
2. $5a^3 - 5a^2$
3. $7n^3 + 6$
4. $-6n^3$
5. $a^2 - 3$
6. $2r^4 + 9r^3$
7. $1$
8. $6x^4 - 6x$
9. $-7k^4 - 11k^2 + 6$
10. $-6n^5 - 2n^4 + 3n + 3$