Determine which of the following expressions represents the area of the rectangle in the drawing:
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Determine which of the following expressions represents the area of the rectangle in the drawing:
The area of a rectangle equals the length multiplied by the width.
Proceed to write the exercise according to the data shown in the drawing:
Solve the exercise using the distributive property.
That is:
Multiply the first term in the left parentheses by the first term in the right parentheses,
Multiply the first term in the left parentheses by the second term in the right parentheses,
Multiply the second term in the left parentheses by the first term in the right parentheses,
Multiply the second term in the left parentheses by the second term in the right parentheses.
As follows:
Let's solve what's inside of the parentheses:
Combine like terms with x to obtain the following:
Check if there's another expression from the list that could potentially match the expression that we obtained.
Note that we can write the expression in another way, by factoring out x and 9 like this:
If we multiply x and 9 by each term in the parentheses we obtain the following
Which is in fact the same equation that we previously obtained.
Therefore, the matching expressions are the third expression and the sixth expression.
3, 6
\( 140-70= \)
Adding gives you the perimeter, not the area! For rectangles, area = length × width, while perimeter = 2(length + width). Always multiply the dimensions for area.
Expand each expression completely and compare the results. Two expressions are equivalent if they have the same coefficients for each power of x when simplified.
FOIL expands (a+b)(c+d) into ac + ad + bc + bd. Factoring does the reverse - it takes an expanded form and rewrites it as a product of factors.
Yes! Pick any value for x (like x=1) and calculate both expressions. If they give the same result, they're likely equivalent. But always verify with complete algebraic expansion too.
This uses the distributive property in reverse. When you distribute x and 9, you get (3x²+5x) + (27x+45) = 3x² + 32x + 45, which matches our FOIL result!
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