Write in Standard Form (-9x^2-2x)-(-9x^2-3x)
The question is asking to express the given algebraic expression in standard form. Standard form refers to a way of writing down algebraic expressions where terms are ordered from highest degree to lowest degree, and similar terms are combined together. In this specific problem, the task is to subtract one polynomial from another and then simplify the result by combining like terms to create a simplified expression written in standard form. To clarify, the polynomials in question are (-9x^2-2x) and (-9x^2-3x), and you are required to perform the subtraction operation on them.
$\left(\right. - 9 x^{2} - 2 x \left.\right) - \left(\right. - 9 x^{2} - 3 x \left.\right)$
Answer
Solution:
Step 1: To express a polynomial in the standard form, first simplify the expression and then order the terms from highest to lowest degree, following the format $a x^{2} + b x + c$.
Step 2: Begin by simplifying the expression.
Step 2.1: Utilize the distributive property to expand the expression: $- 9 x^{2} - 2 x - (- 9 x^{2}) - (- 3 x)$.
Step 2.2: Calculate the product of $-9$ and $-1$: $- 9 x^{2} - 2 x + 9 x^{2} - (- 3 x)$.
Step 2.3: Calculate the product of $-3$ and $-1$: $- 9 x^{2} - 2 x + 9 x^{2} + 3 x$.
Step 3: Proceed to combine like terms.
Step 3.1: Identify and combine like terms in the expression $- 9 x^{2} - 2 x + 9 x^{2} + 3 x$.
Step 3.1.1: Sum the terms $- 9 x^{2}$ and $9 x^{2}$: $- 2 x + 0 + 3 x$.
Step 3.1.2: Sum the terms $- 2 x$ and $0$: $- 2 x + 3 x$.
Step 3.2: Finally, add $- 2 x$ and $3 x$ together to get $x$.
Knowledge Notes:
Standard Form of a Polynomial: A polynomial is in standard form when its terms are ordered from highest to lowest degree. For a quadratic polynomial, the standard form is $a x^{2} + b x + c$, where $a$, $b$, and $c$ are constants, and $a \neq 0$.
Simplifying Expressions: To simplify an algebraic expression, you combine like terms, which are terms that have the same variables raised to the same powers. The coefficients of these terms are added or subtracted.
Distributive Property: This property is used to remove parentheses by multiplying the term outside the parentheses by each term inside. For example, $a(b + c) = ab + ac$.
Combining Like Terms: This involves adding or subtracting coefficients of terms that have the same variable parts. For instance, $2x + 3x = 5x$.
Negative Signs and Parentheses: When simplifying expressions, it's important to correctly handle negative signs in front of parentheses. The negative sign causes a change in sign for each term inside the parentheses when the parentheses are removed.
In this problem, the process involves simplifying the given expression by applying the distributive property to remove parentheses, combining like terms, and writing the result in standard form. The final simplified form of the given polynomial is $x$.
