Show that the area can be written as x² + 3x - 4.
Understand the Problem
The question is asking us to show that the area of a rectangle with length given by (x + 4) and breadth by (x - 1) can be expressed as x² + 3x - 4. To solve this, we will multiply the length by the breadth and rearrange the terms to match the required expression.
Answer
The area can be expressed as $A = x^2 + 3x - 4$.
Answer for screen readers
The area of the rectangle can be expressed as $A = x^2 + 3x - 4$.
Steps to Solve
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Identify the length and breadth The length of the rectangle is given by $L = x + 4$ and the breadth is given by $B = x - 1$.
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Calculate the area To find the area $A$ of a rectangle, use the formula: $$ A = L \times B $$
Substituting the values: $$ A = (x + 4)(x - 1) $$
- Expand the expression Using the distributive property (FOIL method) to expand the equation: $$ A = x(x - 1) + 4(x - 1) $$
This simplifies to: $$ A = x^2 - x + 4x - 4 $$
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Combine like terms Now combine the like terms: $$ A = x^2 + 3x - 4 $$
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Conclude the proof We have shown that the area can be expressed as $A = x^2 + 3x - 4$.
The area of the rectangle can be expressed as $A = x^2 + 3x - 4$.
More Information
This shows how to multiply two binomials to find the area of a rectangle. It's a common method in algebra that helps understand polynomial expansion.
Tips
- Not applying the distributive property correctly: Make sure to multiply each term in the first parenthesis by each term in the second.
- Forgetting to combine like terms: After expanding, remember to collect similar terms to simplify the expression to its final form.
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