We appreciate your visit to Choose the correct simplification of tex 4x 3 3x 2 4x 3 tex A tex 12x 3 25x 2 9 tex B tex 12x 3. 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 simplify
[tex]$$
(4x - 3)(3x^2 - 4x - 3),
$$[/tex]
we can use the distributive property (also known as the FOIL method for binomials) to multiply every term in the first factor by every term in the second factor.
1. First, distribute the term [tex]$4x$[/tex] across the second polynomial:
[tex]$$
4x \cdot 3x^2 = 12x^3,
$$[/tex]
[tex]$$
4x \cdot (-4x) = -16x^2,
$$[/tex]
[tex]$$
4x \cdot (-3) = -12x.
$$[/tex]
2. Next, distribute the term [tex]$-3$[/tex] across the second polynomial:
[tex]$$
-3 \cdot 3x^2 = -9x^2,
$$[/tex]
[tex]$$
-3 \cdot (-4x) = 12x,
$$[/tex]
[tex]$$
-3 \cdot (-3) = 9.
$$[/tex]
3. Now, combine all the products:
[tex]$$
12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9.
$$[/tex]
4. Combine like terms:
- For [tex]$x^3$[/tex]: There is only one term, [tex]$12x^3$[/tex].
- For [tex]$x^2$[/tex]: Combine [tex]$-16x^2$[/tex] and [tex]$-9x^2$[/tex] to get
[tex]$$
-16x^2 - 9x^2 = -25x^2.
$$[/tex]
- For [tex]$x$[/tex]: Combine [tex]$-12x$[/tex] and [tex]$12x$[/tex], which cancel each other out:
[tex]$$
-12x + 12x = 0.
$$[/tex]
- The constant term is [tex]$9$[/tex].
Thus, the simplified expression is
[tex]$$
12x^3 - 25x^2 + 9.
$$[/tex]
Comparing with the given options, the correct answer is:
[tex]$$
12x^3 -25x^2 + 9.
$$[/tex]
[tex]$$
(4x - 3)(3x^2 - 4x - 3),
$$[/tex]
we can use the distributive property (also known as the FOIL method for binomials) to multiply every term in the first factor by every term in the second factor.
1. First, distribute the term [tex]$4x$[/tex] across the second polynomial:
[tex]$$
4x \cdot 3x^2 = 12x^3,
$$[/tex]
[tex]$$
4x \cdot (-4x) = -16x^2,
$$[/tex]
[tex]$$
4x \cdot (-3) = -12x.
$$[/tex]
2. Next, distribute the term [tex]$-3$[/tex] across the second polynomial:
[tex]$$
-3 \cdot 3x^2 = -9x^2,
$$[/tex]
[tex]$$
-3 \cdot (-4x) = 12x,
$$[/tex]
[tex]$$
-3 \cdot (-3) = 9.
$$[/tex]
3. Now, combine all the products:
[tex]$$
12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9.
$$[/tex]
4. Combine like terms:
- For [tex]$x^3$[/tex]: There is only one term, [tex]$12x^3$[/tex].
- For [tex]$x^2$[/tex]: Combine [tex]$-16x^2$[/tex] and [tex]$-9x^2$[/tex] to get
[tex]$$
-16x^2 - 9x^2 = -25x^2.
$$[/tex]
- For [tex]$x$[/tex]: Combine [tex]$-12x$[/tex] and [tex]$12x$[/tex], which cancel each other out:
[tex]$$
-12x + 12x = 0.
$$[/tex]
- The constant term is [tex]$9$[/tex].
Thus, the simplified expression is
[tex]$$
12x^3 - 25x^2 + 9.
$$[/tex]
Comparing with the given options, the correct answer is:
[tex]$$
12x^3 -25x^2 + 9.
$$[/tex]
Thanks for taking the time to read Choose the correct simplification of tex 4x 3 3x 2 4x 3 tex A tex 12x 3 25x 2 9 tex B tex 12x 3. 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
