To find the difference between the two algebraic expressions shown in the activity, we need to subtract the second expression from the first one.
Step 1: Identify the expressions
From the cards in the image, we have:
*
Expression 1: $4x^2 + 2x - 3$ (4 green squares, 2 green rectangles, 3 red small squares)
*
Expression 2: $x^2 + 3x - 2$ (1 green square, 3 green rectangles, 2 red small squares)
Step 2: Set up the subtraction
We want to calculate: $(\text{Expression 1}) - (\text{Expression 2})$
$$ (4x^2 + 2x - 3) - (x^2 + 3x - 2) $$
Step 3: Remove the brackets
When we subtract a group of terms inside brackets, we must change the sign of every term inside the second bracket.
* Positive $x^2$ becomes negative $-x^2$.
* Positive $3x$ becomes negative $-3x$.
* Negative $2$ becomes positive $+2$.
So, the equation becomes:
$$ 4x^2 + 2x - 3 - x^2 - 3x + 2 $$
Step 4: Group like terms
Now, we combine the terms that are the same type ($x^2$ with $x^2$, $x$ with $x$, and numbers with numbers).
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$x^2$ terms: $4x^2 - x^2 = 3x^2$
*
$x$ terms: $2x - 3x = -1x$ (or just $-x$)
*
Number terms: $-3 + 2 = -1$
Step 5: Combine the results
Putting it all together, we get:
$$ 3x^2 - x - 1 $$
Final Answer:
The difference of the algebraic expressions is
3x² - x - 1.
Parent Tip: Review the logic above to help your child master the concept of algebraic expressions projects.
