Look at the rectangle in the figure.
What is its area?
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Look at the rectangle in the figure.
What is its area?
We know that the area of a rectangle is equal to its length multiplied by its width.
We begin by writing an equation with the available data.
Next we use the distributive property to solve the equation.
We then solve each of the exercises within the parentheses:
Finally we add up all the coefficients of X squared and all the coefficients of X cubed and we obtain the following:
\( (x+y)(x-y)= \)
Use the distributive property! Multiply each term in the first expression by each term in the second expression. For , you get 4 products: 4x×8x, 4x×8, x²×8x, x²×8.
That's normal! When you multiply , you get . The final answer should be arranged by decreasing powers: cubic terms first, then quadratic, then linear.
Group terms with the same variable power together. For example: . Add the coefficients (numbers) but keep the variable part the same.
It doesn't matter! Rectangle area is commutative, meaning length × width = width × length. Just make sure you multiply the two expressions representing the sides.
Look at the degree (highest power) and leading coefficient. Also, try substituting a simple value like x=1 into both your answer and the original expression to see if they match.
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