Question

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.

Answer 1

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

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

Answer: 1) Please find attached the diagram showing the answer - 1

Answer: 1) Please find attached the diagram showing the answer - 1

Answer: 1) Please find attached the diagram showing the answer - 2

Explore all similar answers

Answer 2

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

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