Question $\left(x^{4}-3 x\right)\left(5-2 x^{3}+4 x^{4}\right)$

Studdy Solution

STEP 1

1. We are given a polynomial expression in factored form.
2. The goal is to expand the expression by distributing the terms.
3. We will use the distributive property to multiply each term in the first polynomial by each term in the second polynomial.

STEP 2

1. Distribute each term of the first polynomial across each term of the second polynomial.
2. Combine like terms to simplify the expression.

STEP 3

Identify the terms in each polynomial. The first polynomial is $x^4 - 3x$ , and the second polynomial is $5 - 2x^3 + 4x^4$ .

STEP 4

Distribute $x^4$ from the first polynomial across each term in the second polynomial:
$x^4 \times 5 = 5x^4$ $x^4 \times (-2x^3) = -2x^7$ $x^4 \times 4x^4 = 4x^8$

STEP 5

Distribute $-3x$ from the first polynomial across each term in the second polynomial:
$-3x \times 5 = -15x$ $-3x \times (-2x^3) = 6x^4$ $-3x \times 4x^4 = -12x^5$

STEP 6

Combine all the terms obtained from the distribution:
$4x^8 - 2x^7 - 12x^5 + 5x^4 + 6x^4 - 15x$

STEP 7

Combine like terms:
$4x^8 - 2x^7 - 12x^5 + (5x^4 + 6x^4) - 15x$ $= 4x^8 - 2x^7 - 12x^5 + 11x^4 - 15x$
The expanded and simplified expression is:
$\boxed{4x^8 - 2x^7 + 11x^4 - 12x^5 - 15x}$

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