Multiply each expression. − x ( 3 x 2 − 4 x + 2 ) -x(3x^2-4x+2)

Here, we're going to simplify this expression by multiplying this monomial by this polynomial. And to do that, we'll use our distributive property. So we want to take our outside term and multiply it into each of the terms in the sum. Doing that, we'll have negative x times three x squared. Next, we'll have negative x times negative four x. And lastly, we'll have negative x times two. Simplifying, we'll take our negative and multiply it by three to get negative three. And x times x squared makes x cubed. Next, we'll have our negative times negative four, which makes positive four. And x times x will make x squared. And lastly, we have our negative times two, which will make negative two, and x by itself makes x. So this expression simplifies to negative three x cubed plus four x squared minus two x.

6. Exponents and Polynomials

Multiplying Polynomials

Beginning Algebra

6. Exponents and Polynomials

Multiplying Polynomials

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Multiple Choice

Multiply each expression.
$- x (3 x^{2} - 4 x + 2)$

$-3x^3+4x^2-2x$

$3x^3-4x^2+2x$

$-3x^3-4x^2-2x$

$3x^3+4x^2+2x$

Verified step by step guidance

Identify the monomial and the polynomial in the expression you need to multiply. The monomial is a single term (like \$3x$), and the polynomial is a sum of terms (like $2x^2 + 5x - 1$).

Apply the distributive property by multiplying the monomial by each term in the polynomial separately. This means you multiply the coefficients (numbers) together and then multiply the variables using the laws of exponents.

When multiplying variables with the same base, add their exponents. For example, $x^a \times x^b = x^{a+b}$. If a variable does not have an exponent, it is understood to be 1.

Write down each product from the distribution step as a separate term, keeping track of the signs (positive or negative) of each term.

Combine all the terms you obtained from the multiplication to write the final expression as a polynomial. This is the product of the monomial and the polynomial.

3:46m

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Struggling with Beginning Algebra?

Multiply each expression.−x(3x2−4x+2)-x(3x^2-4x+2)

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Multiply each expression.
$- x (3 x^{2} - 4 x + 2)$