Use A Diagram To Show That (3x+1)(x+2) Is Equivalent To 3x2+7x+2. Show Your Work. Is (x+4) Equivalent To 2x2+8x+8? Explain Or Show Your Reasoning.

1) Please find attached the diagram showing the answer to the question

The area of the diagram is (3x + 1)(x + 2) = 3 dark green squares + 7 light green squares + 2 Plain squares

∴ (3x + 1)(x + 2) = 3·x² + 7·x + 2

2) When x = 1, (1 + 4)² = 25 ≠ 2 × 1² + 8 × 1 + 8 = 18

Therefore, (x + 4)² is not equivalent to 2·x² + 8·x + 8

Step-by-step explanation:

1) In the attached diagram, we have;

For x = 1

(3x + 1)(x + 2) = (3 + 1)(1 + 2)

Therefore, the length of the sides of the rectangle are;

Height = 4, and Width = 3

For x = 1, x² = 1² = 1

∴ 3·x² = 3, 7·x = 7 × 1 = 7, and 2 = 2

Therefore, from the diagram, we have;

The area = (3x + 1)(x + 2) = 3 dark green squares + 7 light green squares + 2 Plain squares

∴ (3x + 1)(x + 2) = 3·x² + 7·x + 2

The diagram for when x = 3 is also included

2) For (x + 4)², we have;

When x = 1, (x + 4)² = (1 + 4)² = 25

However;

When x = 1, 2·x² + 8·x + 8 = 2 × 1² + 8 × 1 + 8 = 18

Therefore;

(x + 4)² is not equivalent to 2·x² + 8·x + 8

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

the answer is 1 becuz if it were 1.0 that would rip apart the entire so ya. : )

~potato.

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