A painter buys a canvas with the following dimensions:
How much space to paint does she have?
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A painter buys a canvas with the following dimensions:
How much space to paint does she have?
We calculate the area using the distributive property:
We solve each of the multiplication exercises:
We join the x coefficients:
\( 140-70= \)
Each term in the first binomial (23x + 12) must multiply each term in the second binomial (20x + 7). That gives you: 23x×20x, 23x×7, 12×20x, and 12×7 = four products total!
Use FOIL: First terms (23x×20x), Outer terms (23x×7), Inner terms (12×20x), Last terms (12×7). This ensures you don't miss any!
Both 161x and 240x are like terms (they both have x to the first power). You must combine them: 161x + 240x = 401x to get your final simplified answer.
The x² term comes from multiplying the x terms together: 23x × 20x = 460x². If you get this wrong, double-check that you're multiplying both the numbers (23 × 20 = 460) and the variables (x × x = x²).
Your answer should be a quadratic expression with three terms: an x² term, an x term, and a constant. For this problem: has all three parts ✓
This represents the total area of the canvas the painter can work on. The expression tells us how many square units of space she has to paint.
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