Question

add polynomials
simplify each expression.
$(7c - 5c^4)+(9c - 2c^4 + 3)$ $(5 - 7g^2)+(6g^4 + 2 + 3g^2)$
$(7 + 2s^4)+(4s^5 - 9 - 3s^4)$ $(4h^5 + 2)+(9h^5 - 7 - 5h^2)$
$(2x^4 - 4x^3)+(6x^3 + 9x - 5x^4)$ $(2b + 9 - 7b^3)+(8b^3 - 6 - 4b^5)$
$(2 - 6p^2 - 5p^4)+(9p - 8p^4 + 4)$ $(6z^3 - 9)+(5z^3 - 8 + z^4)$

Explanation:

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1. Simplify $(7c-5c^4)+(9c-2c^4+3)$

Step1: Remove parentheses

$7c - 5c^4 + 9c - 2c^4 + 3$

Step2: Combine like terms

$(-5c^4-2c^4)+(7c+9c)+3 = -7c^4 + 16c + 3$

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2. Simplify $(5-7g^2)+(6g^4+2+3g^2)$

Step1: Remove parentheses

$5 - 7g^2 + 6g^4 + 2 + 3g^2$

Step2: Combine like terms

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

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3. Simplify $(7+2s^4)+(4s^5-9-3s^4)$

Step1: Remove parentheses

$7 + 2s^4 + 4s^5 - 9 - 3s^4$

Step2: Combine like terms

$4s^5+(2s^4-3s^4)+(7-9) = 4s^5 - s^4 - 2$

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4. Simplify $(4h^5 + 2)+(9h^5 - 7 - 5h^2)$

Step1: Remove parentheses

$4h^5 + 2 + 9h^5 - 7 - 5h^2$

Step2: Combine like terms

$(4h^5+9h^5)-5h^2+(2-7) = 13h^5 - 5h^2 - 5$

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5. Simplify $(2x^4-4x^3)+(6x^3+9x-5x^4)$

Step1: Remove parentheses

$2x^4 - 4x^3 + 6x^3 + 9x - 5x^4$

Step2: Combine like terms

$(2x^4-5x^4)+(-4x^3+6x^3)+9x = -3x^4 + 2x^3 + 9x$

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6. Simplify $(2b+9-7b^3)+(8b^3-6-4b^5)$

Step1: Remove parentheses

$2b + 9 - 7b^3 + 8b^3 - 6 - 4b^5$

Step2: Combine like terms

$-4b^5+(-7b^3+8b^3)+2b+(9-6) = -4b^5 + b^3 + 2b + 3$

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7. Simplify $(2-6p^2-5p^4)+(9p-8p^4+4)$

Step1: Remove parentheses

$2 - 6p^2 - 5p^4 + 9p - 8p^4 + 4$

Step2: Combine like terms

$(-5p^4-8p^4)-6p^2+9p+(2+4) = -13p^4 - 6p^2 + 9p + 6$

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8. Simplify $(6z^3 - 9)+(5z^3 - 8 + z^4)$

Step1: Remove parentheses

$6z^3 - 9 + 5z^3 - 8 + z^4$

Step2: Combine like terms

$z^4+(6z^3+5z^3)+(-9-8) = z^4 + 11z^3 - 17$

Answer:

1. $\boldsymbol{-7c^4 + 16c + 3}$
2. $\boldsymbol{6g^4 - 4g^2 + 7}$
3. $\boldsymbol{4s^5 - s^4 - 2}$
4. $\boldsymbol{13h^5 - 5h^2 - 5}$
5. $\boldsymbol{-3x^4 + 2x^3 + 9x}$
6. $\boldsymbol{-4b^5 + b^3 + 2b + 3}$
7. $\boldsymbol{-13p^4 - 6p^2 + 9p + 6}$
8. $\boldsymbol{z^4 + 11z^3 - 17}$