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]
