Answer:
the expanded expression is
�
3
−
64
x
3
−64
Step-by-step explanation:
To expand the expression
(
�
−
4
)
(
�
2
+
4
�
+
16
)
(x−4)(x
2
+4x+16), we'll use the distributive property:
(
�
−
4
)
(
�
2
+
4
�
+
16
)
(x−4)(x
2
+4x+16)
First, distribute
�
x to each term inside the second parentheses:
�
(
�
2
)
+
�
(
4
�
)
+
�
(
16
)
x(x
2
)+x(4x)+x(16)
=
�
3
+
4
�
2
+
16
�
=x
3
+4x
2
+16x
Next, distribute
−
4
−4 to each term inside the second parentheses:
−
4
(
�
2
)
−
4
(
4
�
)
−
4
(
16
)
−4(x
2
)−4(4x)−4(16)
=
−
4
�
2
−
16
�
−
64
=−4x
2
−16x−64
Now, we can combine like terms:
(
�
−
4
)
(
�
2
+
4
�
+
16
)
=
�
3
+
4
�
2
+
16
�
−
4
�
2
−
16
�
−
64
(x−4)(x
2
+4x+16)=x
3
+4x
2
+16x−4x
2
−16x−64
=
�
3
−
64
=x
3
−64
So, the expanded expression is
�
3
−
64
x
3
−64.
