Question

distribute and subtract algebraic expressions
question
written as a simplified polynomial in standard form, what is the result when \\((2x + 7)^2\\) is subtracted from \\(10x^2 - x\\)?
answer attempt 1 out of 2

Explanation:

Step1: Expand \((2x + 7)^2\)

Using the formula \((a + b)^2 = a^2 + 2ab + b^2\), where \(a = 2x\) and \(b = 7\), we get:
\((2x + 7)^2=(2x)^2 + 2\times(2x)\times7 + 7^2 = 4x^2 + 28x + 49\)

Step2: Set up the subtraction

We need to subtract \((2x + 7)^2\) (which we expanded to \(4x^2 + 28x + 49\)) from \(10x^2 - x\). So the expression is:
\((10x^2 - x)-(4x^2 + 28x + 49)\)

Step3: Distribute the negative sign

Distribute the negative sign to each term inside the parentheses:
\(10x^2 - x - 4x^2 - 28x - 49\)

Step4: Combine like terms

Combine the \(x^2\) terms: \(10x^2 - 4x^2 = 6x^2\)
Combine the \(x\) terms: \(-x - 28x = -29x\)
The constant term is \(-49\)
Putting it all together, we get \(6x^2 - 29x - 49\)

Answer:

\(6x^2 - 29x - 49\)