# Divide (b^3*(8b)+8)÷(b-2) (b3⋅(8b)+8)÷(b-2)
Expand b3⋅(8b)+8.
Remove parentheses.
b3⋅(8b)+8b-2
Reorder b3 and 8.
8b3b+8b-2
Add 3 and 1.
8b4+8b-2
8b4+8b-2
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 b – 2 8b4 + 0b3 + 0b2 + 0b + 8
Divide the highest order term in the dividend 8b4 by the highest order term in divisor b.
 8b3 b – 2 8b4 + 0b3 + 0b2 + 0b + 8
Multiply the new quotient term by the divisor.
 8b3 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 + 8b4 – 16b3
The expression needs to be subtracted from the dividend, so change all the signs in 8b4-16b3
 8b3 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 8b3 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3
Pull the next terms from the original dividend down into the current dividend.
 8b3 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2
Divide the highest order term in the dividend 16b3 by the highest order term in divisor b.
 8b3 + 16b2 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2
Multiply the new quotient term by the divisor.
 8b3 + 16b2 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 + 16b3 – 32b2
The expression needs to be subtracted from the dividend, so change all the signs in 16b3-32b2
 8b3 + 16b2 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 8b3 + 16b2 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2
Pull the next terms from the original dividend down into the current dividend.
 8b3 + 16b2 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2 + 0b
Divide the highest order term in the dividend 32b2 by the highest order term in divisor b.
 8b3 + 16b2 + 32b b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2 + 0b
Multiply the new quotient term by the divisor.
 8b3 + 16b2 + 32b b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2 + 0b + 32b2 – 64b
The expression needs to be subtracted from the dividend, so change all the signs in 32b2-64b
 8b3 + 16b2 + 32b b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2 + 0b – 32b2 + 64b
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 8b3 + 16b2 + 32b b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2 + 0b – 32b2 + 64b + 64b
Pull the next terms from the original dividend down into the current dividend.
 8b3 + 16b2 + 32b b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2 + 0b – 32b2 + 64b + 64b + 8
Divide the highest order term in the dividend 64b by the highest order term in divisor b.
 8b3 + 16b2 + 32b + 64 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2 + 0b – 32b2 + 64b + 64b + 8
Multiply the new quotient term by the divisor.
 8b3 + 16b2 + 32b + 64 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2 + 0b – 32b2 + 64b + 64b + 8 + 64b – 128
The expression needs to be subtracted from the dividend, so change all the signs in 64b-128
 8b3 + 16b2 + 32b + 64 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2 + 0b – 32b2 + 64b + 64b + 8 – 64b + 128
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 8b3 + 16b2 + 32b + 64 b – 2 8b4 + 0b3 + 0b2 + 0b + 8 – 8b4 + 16b3 + 16b3 + 0b2 – 16b3 + 32b2 + 32b2 + 0b – 32b2 + 64b + 64b + 8 – 64b + 128 + 136
The final answer is the quotient plus the remainder over the divisor.
8b3+16b2+32b+64+136b-2
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