Question

question 6
expand the expression to a polynomial in standard form:
(-4x - 3)(3x² - x - 1)
answer
attempt 1 out of 2
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time remaining: 116 mins

Explanation:

Step1: Apply distributive property

Multiply \(-4x\) and \(-3\) with each term in \(3x^2 - x - 1\) separately.
First, multiply \(-4x\) with \(3x^2 - x - 1\):
\(-4x \times 3x^2 = -12x^3\), \(-4x \times (-x) = 4x^2\), \(-4x \times (-1) = 4x\)
Then, multiply \(-3\) with \(3x^2 - x - 1\):
\(-3 \times 3x^2 = -9x^2\), \(-3 \times (-x) = 3x\), \(-3 \times (-1) = 3\)

Step2: Combine like terms

Now, combine the terms we got:
\(-12x^3 + 4x^2 + 4x - 9x^2 + 3x + 3\)
Combine the \(x^2\) terms: \(4x^2 - 9x^2 = -5x^2\)
Combine the \(x\) terms: \(4x + 3x = 7x\)
So the polynomial becomes \(-12x^3 - 5x^2 + 7x + 3\)

Answer:

\(-12x^3 - 5x^2 + 7x + 3\)