Question

combining polynomials in exercises 41–54, perform the indicated operations and simplify.

1. $(6x - 5) - (8x + 15)$
2. $(2x^2 + 1) + (x^2 - 2x + 1)$
3. $-(x^3 - 2) + (4x^3 - 2x)$
4. $-(2x^2 - 3) + (4x^2 - 2x)$
5. $2(x^4 + 2x) + (5x + 2)$
6. $(z^4 - 2z^2) + 3(z^4 + 4)$
7. $5z - 3z - (10z + 8)$
8. $9w^2 - 2w - (w^2 + 3w)$
9. $(y^3 + 1) - (y^2 + 1) + (3y - 7)$
10. $(a^2 - a) - (2a^2 + 3a) - (5a^2 - 12)$
11. $2(t^2 + 5) - 3(t^2 + 5) + 5(t^2 + 5)$
12. $-10(v + 2) + 8(v - 1) - 3(v - 9)$
13. $8v - 6(3v - v^2) + 10(10v + 3)$
14. $3(x^2 - 2x + 3) - 4(4x + 1) - (3x^2 - 2x)$

Explanation:

Exercise 41

Step1: Distribute the negative sign

$6x - 5 - 8x - 15$

Step2: Combine like terms

$(6x-8x)+(-5-15)$

Step1: Remove parentheses

$2x^2 + 1 + x^2 - 2x + 1$

Step2: Combine like terms

$(2x^2+x^2)-2x+(1+1)$

Step1: Distribute the negative sign

$-x^3 + 2 + 4x^3 - 2x$

Step2: Combine like terms

$(-x^3+4x^3)-2x+2$

Answer:

$-2x - 20$

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Exercise 42