One term times another
A plot of land is 3x metres by 4x metres. Here x stands for a number. What is its area?
3x tall, 4x wide. Step 1 of 4
- Rectangle:
3xtall,4xwide. - A grid of x-by-x squares: 3 rows, 4 columns.
- Each cell is
x × x = x². - Count them: 12 cells →
12x².
Its area is 12x² square metres.
Write letters side by side to multiply them. x times x is x², meaning x × x.
Rule: multiply the coefficients. Write the letters side by side. A letter used twice becomes squared.
At x = 2 one side is 3 × 2 = 6 metres. The other is 4 × 2 = 8 metres. The area is 6 × 8 = 48 square metres. And 12x² is 12 × 4 = 48.
Different letters are written side by side. Here 2 × 3 = 6, so 2a × 3b = 6ab.
Slide x. Count the squares.
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