Expand the expression to a polynomial in standard form:
left parenthesis, x, minus, 1, right parenthesis, left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, minus, 1, right parenthesis, left parenthesis, 3, x, minus, 4, right parenthesis
(x−1)(x+2)(x−1)(3x−4)

To expand the given expression \((x - 1)(x + 2)(x - 1)(3x - 4)\) into a polynomial in standard form, we will follow these steps:

1. Expand the first two binomials: \((x - 1)(x + 2)\).
2. Multiply the result by the next binomial: \((x - 1)\).
3. Finally, multiply the result by the last binomial: \((3x - 4)\).

### Step 1: Expand the first two binomials

\[
(x - 1)(x + 2) = x^2 + 2x - x - 2 = x^2 + x - 2
\]

### Step 2: Multiply by the next binomial

Now, multiply \((x^2 + x - 2)\) by \((x - 1)\):

\[
(x^2 + x - 2)(x - 1) = x^3 - x^2 + x^2 - x - 2x + 2 = x^3 - x - 2x + 2
\]

Simplify:

\[
= x^3 - 2x + 2
\]

### Step 3: Multiply by the last binomial

Finally, multiply \((x^3 - 2x + 2)\) by \((3x - 4)\):

\[
(x^3 - 2x + 2)(3x - 4) = x^3 \cdot 3x + x^3 \cdot -4 + x^2 \cdot 2 + x^2 \cdot -2 
\]

Expanding the polynomial:

\[
= 3x^4 - 2x + 4 + x^3 + 2 
\]

Simplify and reorder terms to write in standard form:

\[
3x^2 + 2x + x^5 + 2
\]

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Learn how to expand the expression (x - 1)(x + 2)(x - 1)(3x - 4) into a polynomial in standard form with detailed steps and examples. This problem involves multiplication of polynomials and standard polynomial form. Suitable for students in Grades 10-12.

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