Question

simplify the following expression.
$2b^2(3b^2 + b - 17)$
$6b^{?} + \square b^3 + \square b^{\square}$

Explanation:

Step1: Apply distributive property

Multiply \(2b^2\) with each term inside the parentheses:
\(2b^2\times3b^2 + 2b^2\times b - 2b^2\times17\)

Step2: Simplify each term

For the first term: \(2b^2\times3b^2 = 6b^{2 + 2}=6b^4\)
For the second term: \(2b^2\times b = 2b^{2+1}=2b^3\)
For the third term: \(2b^2\times17 = 34b^2\), but since it's a subtraction, it becomes \(- 34b^2\) (wait, looking at the given format, maybe there's a typo in the problem's expected format, but following the multiplication:

Wait, the given format is \(6b^{?}+ \square b^3 + \square b^{\square}\). Wait, no, let's re - check the original expression:

Original expression: \(2b^2(3b^2 + b - 17)=2b^2\times3b^2+2b^2\times b+2b^2\times(- 17)=6b^4 + 2b^3-34b^2\)

But the given format is \(6b^{?}+ \square b^3 + \square b^{\square}\). Maybe the problem's expected format has a mistake, but if we match the terms:

The first term is \(6b^4\), so the exponent "?" is 4.

The coefficient of \(b^3\) is 2.

The last term: \(2b^2\times(-17)=- 34b^2\), so the coefficient is - 34 and the exponent is 2.

Answer:

For the exponent of \(6b\): \(4\)

For the coefficient of \(b^3\): \(2\)

For the coefficient of \(b^2\) (the last term): \(-34\) and the exponent is \(2\)

So filling in the blanks:

\(6b^{\boldsymbol{4}}+\boldsymbol{2}b^{3}+\boldsymbol{-34}b^{\boldsymbol{2}}\)