Question

Solve and Show ALL steps
|–4b – 8| + |–1 – b²| + 2b³ ; b = –2

Answer 1

|–4b – 8| + |–1 – b²| + 2b³
Substitute all of the b variables for -2.
|–4(-2)– 8| + |–1 – (-2)²| + 2(-2)³
Multiply the exponents
|–4(-2) – 8| + |–1 – 4| + 2(-8)
Multiply the variable number (-2) by the coefficent
|8 – 8| + |–1 – 4| + (-16)
Subtract 8 from 8
|0| +|-1 - 4| + (-16)
Subtract -4 from -1
|0| |- 5| + (-16)
Use the absolute value tool on 0 and -5
0 + 5 - 16
Add 5 to 0
5 - 16
Subtract
Final Answer: -11

Answer 2

`|a|= \left\{\begin{array}{ccc}a&for\ a\geq0\\-a&for\ a \ \textless \ 0\end{array}\right\\\\Examples:\\\\|2|=2\ because\ 2\geq0\\|0|=0\ because\ 0\geq0\\|-5|=-(-5)=5\ because\ -5 \ \textless \ 0\\|-11|=11\ because\ -11 \ \textless \ 0\\|-2.5|=2.5\ because\ -2.5 \ \textless \ 0`


`|-4b-8|+|-1-b^2|+2b^3\\\\subtitute\ the\ value\ of\ b=-2\ to\ the\ expression:\\\\|-4\cdot(-2)-8|+|-1-(-2)^2|+2\cdot(-2)^3\\\\=|8-8|+|-1-4|+2\cdot(-8)\\\\=|0|+|-5|-16\\\\=0+5-16\\\\=-11`