Simplify 9x^2+7x-2-8x-10

The given problem is a mathematical expression that needs to be simplified. Specifically, it's a polynomial that includes terms with a variable 'x' raised to the power of 2 (squared terms), terms with the variable 'x' to the power of 1 (linear terms), and constant terms (numbers without any variable). The problem asks to combine like terms and rearrange the expression to its simplest form by performing the arithmetic operations of addition and subtraction.

$9 x^{2} + 7 x - 2 - 8 x - 10$

Answer

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Solution:

Step 1:

Combine like terms by subtracting $8x$ from $7x$. The resulting expression is $9x^2 - x - 2 - 10$.

Step 2:

Next, subtract $10$ from $-2$. This simplifies the expression to $9x^2 - x - 12$.

Knowledge Notes:

The problem involves simplifying a polynomial expression by combining like terms. Like terms are terms that have the same variable raised to the same power. Here are the relevant knowledge points:

Combining Like Terms: This is the process of adding or subtracting coefficients of terms that have the same variable and exponent. For example, $ax^n + bx^n = (a+b)x^n$.
Subtraction of Polynomials: When subtracting polynomials, you subtract the coefficients of like terms. For example, if you have $cx^n - dx^n$, the result is $(c-d)x^n$.
Order of Operations: When simplifying expressions, it is important to follow the order of operations. However, since this problem only involves addition and subtraction, we can combine like terms in any order.
Constants: These are terms without variables. In the expression $9x^2 + 7x - 2 - 8x - 10$, the constants are $-2$ and $-10$. They can be combined by simple addition or subtraction.

In the given problem, we first identify and combine the terms with the variable $x$ ($7x$ and $-8x$). Then, we combine the constants ($-2$ and $-10$). The variable terms are combined by subtracting their coefficients, and the constants are combined by subtracting their values. The final expression is in the form $ax^2 + bx + c$, which is a standard form for a quadratic expression.