We appreciate your visit to Multiply the polynomials tex left 8x 2 6x 8 right 6x 5 tex A tex 48x 3 76x 2 18x 40 tex B tex 48x. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To multiply the polynomials
$$\left(8x^2 + 6x + 8\right)(6x - 5),$$
we use the distributive property (also known as the FOIL method for two binomials, but here we extend it as needed).
1. Multiply each term in the first polynomial by each term in the second polynomial:
- Multiply $8x^2$ by $6x$:
$$8x^2 \cdot 6x = 48x^3.$$
- Multiply $8x^2$ by $-5$:
$$8x^2 \cdot (-5) = -40x^2.$$
- Multiply $6x$ by $6x$:
$$6x \cdot 6x = 36x^2.$$
- Multiply $6x$ by $-5$:
$$6x \cdot (-5) = -30x.$$
- Multiply $8$ by $6x$:
$$8 \cdot 6x = 48x.$$
- Multiply $8$ by $-5$:
$$8 \cdot (-5) = -40.$$
2. Now, combine the like terms:
- The only $x^3$ term is:
$$48x^3.$$
- Combine the $x^2$ terms:
$$-40x^2 + 36x^2 = -4x^2.$$
- Combine the $x$ terms:
$$-30x + 48x = 18x.$$
- The constant term is:
$$-40.$$
3. Write the final simplified polynomial by putting the terms together:
$$48x^3 - 4x^2 + 18x - 40.$$
This matches the expression in Option C.
$$\left(8x^2 + 6x + 8\right)(6x - 5),$$
we use the distributive property (also known as the FOIL method for two binomials, but here we extend it as needed).
1. Multiply each term in the first polynomial by each term in the second polynomial:
- Multiply $8x^2$ by $6x$:
$$8x^2 \cdot 6x = 48x^3.$$
- Multiply $8x^2$ by $-5$:
$$8x^2 \cdot (-5) = -40x^2.$$
- Multiply $6x$ by $6x$:
$$6x \cdot 6x = 36x^2.$$
- Multiply $6x$ by $-5$:
$$6x \cdot (-5) = -30x.$$
- Multiply $8$ by $6x$:
$$8 \cdot 6x = 48x.$$
- Multiply $8$ by $-5$:
$$8 \cdot (-5) = -40.$$
2. Now, combine the like terms:
- The only $x^3$ term is:
$$48x^3.$$
- Combine the $x^2$ terms:
$$-40x^2 + 36x^2 = -4x^2.$$
- Combine the $x$ terms:
$$-30x + 48x = 18x.$$
- The constant term is:
$$-40.$$
3. Write the final simplified polynomial by putting the terms together:
$$48x^3 - 4x^2 + 18x - 40.$$
This matches the expression in Option C.
Thanks for taking the time to read Multiply the polynomials tex left 8x 2 6x 8 right 6x 5 tex A tex 48x 3 76x 2 18x 40 tex B tex 48x. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
