Question

box method level 1 (guided)
score: 0/5 penalty: 1 off
question
use the box method to distribute and simplify \\((x - 3)(-5x + 1)\\). drag and drop the terms to the correct locations of the table.
\\((x - 3)\left(-5x + 1\
ight)\\)
answer attempt 1 out of 2
you must answer all questions above in order to submit.

Explanation:

Step1: Create the box

Draw a 2x2 box. The first binomial \((x - 3)\) will be along the top (or left) and the second binomial \((-5x + 1)\) along the side (or top). So the top row cells will be multiplied by \(x\) and \(-3\) (from the first binomial), and the side column cells will be \(-5x\) and \(1\) (from the second binomial).

Step2: Multiply the terms

• Multiply \(x\) (top left) with \(-5x\) (side top): \(x\times(-5x)= -5x^{2}\)
• Multiply \(x\) (top left) with \(1\) (side bottom): \(x\times1 = x\)
• Multiply \(-3\) (top right) with \(-5x\) (side top): \(-3\times(-5x)=15x\)
• Multiply \(-3\) (top right) with \(1\) (side bottom): \(-3\times1=-3\)

Step3: Combine like terms

Now we have the terms \(-5x^{2}\), \(x\), \(15x\), and \(-3\). Combine the like terms (\(x\) and \(15x\)): \(x + 15x=16x\)

Step4: Write the simplified form

Putting it all together, we get \(-5x^{2}+16x - 3\)

Answer:

\(-5x^{2}+16x - 3\)