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Question

1. simplify
(6y^2+4y-3) + (3y^2+2)

2. simplify
(3x^2-5x+8) - (x^2 + 4x+1)

3. multiply and simplify
-3x^3(x^5-x)

4. Mulitply and simplify:
(x-2) (x-2)

5. Mulitply and simplify:
(x+1) (x^2 + 3x-4)


Thanks

Answer 1

1. Addition is commutative, no parenthesis needed. 6y^2 + 4y - 3 + 3y^2 + 2. 6y^2 and 3y^2 combine to 9y^2, and -3 and 2 combine to -1. So, the answer is 9y^2 + 4y - 1.

2. View this as (3x^2 - 5x + 8) + -1(x^2 + 4x + 1). Multiply out -1(x^2 + 4x + 1) by the distributive property, and get (3x^2 - 5x + 8) + (-x^2 - 4x - 1). Remove parenthesis, like in Question 1, and combine like terms. The answer is 2x^2 -9x + 7.

3. 'Tis the distributive property, like used in question 2. Multiply -3x^3 by both x^5 and -x, then add them. -3x^3(x^5) + -x(-3x^3) simplifies to -3x^8 (since you add exponents when multiplying) + 3x^4. -3x^8 + 3x^4.

4. Same as above, only with both terms now. xx - 2x - 2x + -2(-2) is the answer, which simplifies to x^2 - 4x + 4.

5. Same as #4. xx^2 + 3xx - 4x + 1x^2 + 1(3x) - 1(4). That simplifies to x^3 + 3x^2 - 4x + x^2 + 3x - 4, which simplifies again tp x^3 + 4x^2 - x - 4.

Answer 2

1)9y^2+4y-1
2)2x^2-9x+7
3)-3x^8+3x^4
4)x^2-4x+4
5)x^3-4x^2-x+4