Simplify -7x-9 from -4x^2+3x-5

The given problem is asking to perform a simplification process on the algebraic expression "-7x-9" which is to be subtracted from the quadratic expression "-4x^2+3x-5." Essentially, one is to carry out the subtraction of the entire linear expression "-7x-9" from each term of the quadratic expression, which involves combining like terms and simplifying as necessary.

$- 7 x - 9$ from $- 4 x^{2} + 3 x - 5$

Answer

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Solution:

Step 1

Express the given problem algebraically as $- 4 x^{2} + 3 x - 5 - (- 7 x - 9)$ .

Step 2

Begin simplifying the expression term by term.

Step 2.1

Utilize the distributive property to remove parentheses: $- 4 x^{2} + 3 x - 5 + 7 x + 9$ .

Step 2.2

Change the sign of $- 7$ multiplied by $- 1$ : $- 4 x^{2} + 3 x - 5 + 7 x + 9$ .

Step 2.3

Change the sign of $- 9$ multiplied by $- 1$ : $- 4 x^{2} + 3 x - 5 + 7 x + 9$ .

Step 3

Combine like terms to further simplify the expression.

Step 3.1

Combine the $3 x$ and $7 x$ terms: $- 4 x^{2} + 10 x - 5 + 9$ .

Step 3.2

Combine the constants $- 5$ and $9$ : $- 4 x^{2} + 10 x + 4$ .

Knowledge Notes:

To simplify an algebraic expression, one must follow a systematic approach:

Distributive Property: This property states that $a (b + c) = a b + a c$ . It is used to eliminate parentheses by distributing the multiplication over addition or subtraction within the parentheses.
Combining Like Terms: Terms that have the same variable raised to the same power are called like terms. These can be combined by adding or subtracting their coefficients. For example, $3 x$ and $7 x$ are like terms and can be combined to give $10 x$ .
Sign Change: When subtracting a negative term, the double negative becomes a positive. For example, subtracting $- 7 x$ is the same as adding $7 x$ .
Simplification: The process of combining like terms and applying the distributive property to reduce an expression to its simplest form.
Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions. This means handling parentheses first, followed by exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).

In this particular problem, the expression is simplified by first applying the distributive property to remove the parentheses and then combining like terms to arrive at the simplified form of the expression.