![To simplify the expression \((b^2 - 2b + 4)(b - 2)\), we can use the distributive property (also known as the FOIL method for binomials).
1. Multiply each term in the first expression by each term in the second expression:
\[
(b^2)(b) + (b^2)(-2) + (-2b)(b) + (-2b)(-2) + (4)(b) + (4)(-2)
\]
2. This expands to:
\[
b^3 - 2b^2 - 2b^2 + 4b + 4b - 8
\]
3. Combine like terms:
\[
b^3 - 4b^2 + 8b - 8
\]
So, the simplified expression is:
\[
\boxed{b^3 - 4b^2 + 8b - 8}
\]](https://theinternetioimages-f2htc2ggcrath6d7.z01.azurefd.net/$web/askai/3fcd68dd-949d-4816-89a3-0fc4a0ba3e8f.webp)
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To simplify the expression \((b^2 - 2b + 4)(b - 2)\), you need to distribute each term in the first polynomial across each term in the second polynomial. Here's a step-by-step method using the distributive property: 1. Distribute \(b^2\) across \((b - 2)\): \[ b^2 \cdot (b - 2) = b^2 \cdot b + b^2 \cdot (-2) = b^3 - 2b^2 \] 2. Distribute \(-2b\) across \((b - 2)\): \[ -2b \cdot (b - 2) = -2b \cdot b + -2b \cdot (-2) = -2b^2 + 4b \] 3. Distribute \(4\) across \((b - 2)\): \[ 4 \cdot (b - 2) = 4 \cdot b + 4 \cdot (-2) = 4b - 8 \] Now, sum all the distributed terms together: \[ b^3 - 2b^2 - 2b^2 + 4b + 4b - 8 \] Combine the like terms: \[ b^3 + (-2b^2 - 2b^2) + (4b + 4b) - 8 = b^3 - 4b^2 + 8b - 8 \] So, the simplified form of the expression \((b^2 - 2b + 4)(b - 2)\) is: \[ b^3 - 4b^2 + 8b - 8 \]
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