Multiply each expression.(3x2−5x+3)2x2(3x^2-5x+3)2x^2

6 x 4 − 10 3 + 6 x 2 6x^4-10^3+6x^2

Multiply each expression. ( 3 x 2 − 5 x + 3 ) 2 x 2 (3x^2-5x+3)2x^2

this problem, we want to multiply these expressions, our monomial two x squared, by our polynomial three x squared minus five x plus three. And to do this, we're going to use our Distributive Property. Even though our monomial is on the right hand side, we can still use this property and distribute it in by multiplying it by each of the terms in this sum. So doing that, we'll get two x squared times three x squared plus two x squared times negative five x, plus two x squared times three. Simplifying, we'll combine all of our common factors. So, first we have two times three, which makes six, and then x squared times x squared makes x to the fourth power. Next, we'll have two times negative five, which makes negative 10, and x squared times x is x cubed. And lastly, we have two times three, which makes six, and x squared by itself is x squared. So this expression simplifies to 6x to the fourth power minus 10x cubed plus 6x squared.

Multiply each expression. ( 3 x 2 − 5 x + 3 ) 2 x 2 (3x^2-5x+3)2x^2

6 x 4 − 10 3 + 6 x 2 6x^4-10^3+6x^2

6 x 4 + 10 x 3 + 6 x 2 6x^4+10x^3+6x^2

6 x 3 − 10 x 2 + 6 x 6x^3-10x^2+6x

6 x 4 − 10 x 2 + 6 x 6x^4-10x^2+6x

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1. Review of Real Numbers1h 33m

Evaluating Exponents
15m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Simplifying Expressions
44m

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Solving Linear Equations
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Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
42m

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Introduction to Problem Solving
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Percent Problem Solving
36m

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32m

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25m

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13m

Introduction to Relations and Functions
25m

Function Notation
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29m

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17m

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6m

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5m

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38m

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Factoring Trinomials of the Form ax² + bx + c
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14m

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11m

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19m

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Introduction to Complex Numbers
18m

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51m

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40m

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6. Exponents, Polynomials, and Polynomial Functions

Multiplying Polynomials

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

Multiplying Polynomials

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Multiple Choice

Multiply each expression.
$(3 x^{2} - 5 x + 3) 2 x^{2}$

$6 x^{4} + 10 x^{3} + 6 x^{2}$

$6 x^{3} - 10 x^{2} + 6 x$

$6 x^{4} - 10 x^{2} + 6 x$

$6 x^{4} - 10^{3} + 6 x^{2}$

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Verified step by step guidance

Identify the expression to multiply: $(3x^2 - 5x + 3) \times 2x^2$.

Distribute the \$2x^2$ to each term inside the parentheses separately, using the distributive property: multiply $2x^2$ by $3x^2$, then by $-5x$, and finally by $3$.

Multiply the coefficients (numbers) together and apply the laws of exponents for the variable $x$: when multiplying powers with the same base, add the exponents, e.g., $x^a \times x^b = x^{a+b}$.

Write each product as a term: \$2 \times 3 = 6$ and $x^2 \times x^2 = x^{2+2} = x^4$, so the first term is $6x^4$. Repeat this for the other terms.

Combine all the terms to form the final expression: \$6x^4 - 10x^3 + 6x^2$.

3:46m

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