Question

points) part a complete the diamond problems below. each problem is worth 1 pearl
complete the diamond problems. the top cell contains the product of the numbers in the left and right cells, while the bottom cell contains the sum.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
b perform the indicated operation. each is worth 2 points. show your work as necessary. 1) add 4 - 2 + 3 - 5 - 2

1. subtract ( - 2 + 1) - ( + 1)

Explanation:

Part A:

Step1: Calculate product (top)

For each diamond, top = left × right

Step2: Calculate sum (bottom)

For each diamond, bottom = left + right

(1)

Step1: Compute top (product)

$10 \times 3 = 30$

Step2: Compute bottom (sum)

$10 + 3 = 13$

(2)

Step1: Compute top (product)

$5 \times (-2) = -10$

Step2: Compute bottom (sum)

$5 + (-2) = 3$

(3)

Step1: Compute top (product)

$8 \times 7 = 56$

Step2: Compute bottom (sum)

$8 + 7 = 15$

(4)

Step1: Compute top (product)

$12 \times 10 = 120$

Step2: Compute bottom (sum)

$12 + 10 = 22$

(5)

Step1: Compute top (product)

$8 \times 5 = 40$

Step2: Compute bottom (sum)

$8 + 5 = 13$

(6)

Step1: Compute top (product)

$4 \times (-4) = -16$

Step2: Compute bottom (sum)

$4 + (-4) = 0$

(7)

Step1: Compute top (product)

$7 \times 6 = 42$

Step2: Compute bottom (sum)

$7 + 6 = 13$

(8)

Step1: Compute top (product)

$-7 \times 9 = -63$

Step2: Compute bottom (sum)

$-7 + 9 = 2$

1) Addition

Step1: Remove parentheses

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

Step2: Combine like terms

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

Step3: Simplify terms

$6x^2 - 7x$

2) Subtraction

Step1: Distribute the negative sign

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

Step2: Combine like terms

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

Step3: Simplify terms

$x^2 - x$

Answer:

(Part A):

1. Top: $30$, Bottom: $13$
2. Top: $-10$, Bottom: $3$
3. Top: $56$, Bottom: $15$
4. Top: $120$, Bottom: $22$
5. Top: $40$, Bottom: $13$
6. Top: $-16$, Bottom: $0$
7. Top: $42$, Bottom: $13$
8. Top: $-63$, Bottom: $2$

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Part B: