Question

one number is 2 more than another. the difference between their squares is 32. what are the numbers?

answer
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smaller number =

larger number =

Explanation:

Define variables for the two numbers

Using the Difference of Squares Word Problems knowledge point
Let \(x\) represent the smaller number.
The larger number is \(x + 2\).

Set up the difference of squares equation

Using the Difference of Squares Word Problems knowledge point

$$ (x + 2)^2 - x^2 = 32 $$

Expand and simplify the equation

Using the Difference of Squares Word Problems knowledge point

$$
LATEXBLOCK0
$$

Solve for the smaller number

Using the Difference of Squares Word Problems knowledge point

$$
LATEXBLOCK1
$$

Find the larger number

Using the Difference of Squares Word Problems knowledge point

$$ x + 2 = 7 + 2 = 9 $$

Answer:

One number is 2 more than another. The difference between their squares is 32. What are the numbers?

smaller number = <blank>7</blank>

larger number = <blank>9</blank>