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Answer:
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
