Question

i can add, subtract, and multiply polynomials.
(lesson 17.2) add the polynomials. simplify as much as possible. (1 point)

1. $(6s^{3}+9s + 10)$ and $(3s^{3}+4s - 10)$

(lesson 17.2) model the situation with the sum of polynomials. simplify their sum. (1 point)

1. vincent is going to frame a rectangular picture with the dimensions shown.

write a polynomial for the perimeter of the frame, and then simplify.
$5a + 3b$
$2a - 2b$

(lesson 17.3) find each difference. (1 point each)

1. $(6y^{4}+3y^{2}-7)-(12y^{4}-y^{2}+5)$
2. $3(x - 5)-(2x + 4)$

lifelong learning
algebra 1b
credit 2
l4l-

Explanation:

Step1: Add like terms (problem7)

$(6s^3 + 3s^3) + (9s + 4s) + (10 - 10)$

Step2: Simplify each term group (problem7)

$9s^3 + 13s + 0$

Step3: Recall rectangle perimeter formula (problem8)

$P = 2(\text{length} + \text{width})$

Step4: Substitute given dimensions (problem8)

$P = 2[(5a+3b) + (2a-2b)]$

Step5: Combine like terms inside brackets (problem8)

$P = 2(7a + b)$

Step6: Distribute the 2 (problem8)

$P = 14a + 2b$

Step7: Distribute the negative sign (problem9)

$6y^4 + 3y^2 - 7 - 12y^4 + y^2 - 5$

Step8: Combine like terms (problem9)

$(6y^4-12y^4)+(3y^2+y^2)+(-7-5)$

Step9: Simplify each term group (problem9)

$-6y^4 + 4y^2 - 12$

Step10: Distribute the 3 (problem10)

$3x - 15 - (2x + 4)$

Step11: Distribute the negative sign (problem10)

$3x - 15 - 2x - 4$

Step12: Combine like terms (problem10)

$(3x-2x)+(-15-4)$

Step13: Simplify each term group (problem10)

$x - 19$

Answer:

1. $9s^3 + 13s$
2. $14a + 2b$
3. $-6y^4 + 4y^2 - 12$
4. $x - 19$