The algebraic expression for: a number and 9 times its square is
Understand the Problem
The question is asking for the algebraic representation of the phrase 'a number and 9 times its square'. This implies we need to express a variable (representing 'a number') and its square, multiplied by 9, in a mathematical form.
Answer
The algebraic representation is \( x + 9x^2 \).
Answer for screen readers
The algebraic representation is ( x + 9x^2 ).
Steps to Solve
- Define the variable for 'a number'
Let the variable ( x ) represent 'a number'.
- Express the square of the number
The square of the number ( x ) is represented as ( x^2 ).
- Multiply the square by 9
To find 9 times the square of the number, multiply the square ( x^2 ) by 9, which gives us ( 9x^2 ).
- Combine both parts
Now, combine the variable ( x ) with ( 9x^2 ). This represents 'a number and 9 times its square'.
Thus, we can write the expression as follows:
$$ x + 9x^2 $$
The algebraic representation is ( x + 9x^2 ).
More Information
This expression ( x + 9x^2 ) captures both components: the variable ( x ) (the number) and 9 times its square ( 9x^2 ). The combination of these two parts accurately reflects the original phrase.
Tips
- A common mistake is forgetting to include both the number and the term that involves its square. It's important to make sure both parts are represented in the final expression.
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