expand the expression to a polynomial in standard form: (2x - 1)(2x² - x + 7)

Explanation:

Step1: Use distributive property

$$ \begin{align*} &(2x - 1)(2x^{2}-x + 7)\ =&2x(2x^{2}-x + 7)-1(2x^{2}-x + 7) \end{align*} $$

Step2: Distribute (2x) and (-1)

$$ \begin{align*} &2x\times2x^{2}-2x\times x+2x\times7-1\times2x^{2}+1\times x - 1\times7\ =&4x^{3}-2x^{2}+14x-2x^{2}+x - 7 \end{align*} $$

Step3: Combine like - terms

$$ \begin{align*} &4x^{3}+(-2x^{2}-2x^{2})+(14x + x)-7\ =&4x^{3}-4x^{2}+15x - 7 \end{align*} $$

Answer:

(4x^{3}-4x^{2}+15x - 7)