$(15 x^2-2 x+3)-(5+6 x+7 x^2)$

To simplify the expression ( 15 x 2 − 2 x + 3 ) − ( 5 + 6 x + 7 x 2 ) , we first distribute the negative sign, group like terms, and combine them. The final simplified expression is 8 x 2 − 8 x − 2 .
;

Answered by Anonymous | 2025-07-08

Distribute the negative sign: 15 x 2 − 2 x + 3 − 5 − 6 x − 7 x 2 .
Group like terms: ( 15 x 2 − 7 x 2 ) + ( − 2 x − 6 x ) + ( 3 − 5 ) .
Combine the coefficients: 8 x 2 − 8 x − 2 .
The simplified expression is 8 x 2 − 8 x − 2 ​ .

Explanation

Understanding the Problem We are given the expression ( 15 x 2 − 2 x + 3 ) − ( 5 + 6 x + 7 x 2 ) . Our goal is to simplify this expression by combining like terms.

Distributing the Negative Sign First, we distribute the negative sign in the second parenthesis: 15 x 2 − 2 x + 3 − 5 − 6 x − 7 x 2

Grouping Like Terms Next, we group like terms: ( 15 x 2 − 7 x 2 ) + ( − 2 x − 6 x ) + ( 3 − 5 )

Combining Like Terms Now, we combine the coefficients of the like terms:


For the x 2 terms: 15 x 2 − 7 x 2 = 8 x 2 For the x terms: − 2 x − 6 x = − 8 x For the constant terms: 3 − 5 = − 2
So, the simplified expression is: 8 x 2 − 8 x − 2

Final Answer Therefore, the simplified polynomial expression is 8 x 2 − 8 x − 2 ​ .

Examples
Polynomials are used to model curves and shapes in various fields, such as engineering, computer graphics, and economics. For example, engineers use polynomials to design bridges and buildings, while economists use them to model economic growth. Simplifying polynomial expressions, like the one in this problem, is a fundamental skill in these applications. Imagine you're designing a curved ramp for a skate park. You can use a polynomial to represent the shape of the ramp, and simplifying that polynomial helps you understand and control the ramp's curvature and steepness.

Answered by GinnyAnswer | 2025-07-08