(x−5)(x+2)(x−1)

(2x+3)(x−4)(x+5)(2x + 3)(x - 4)(x + 5)(2x+3)(x−4)(x+5)

(x+6)(x−2)(x+3)(x + 6)(x - 2)(x + 3)(x+6)(x−2)(x+3)

(3x−1)(x+4)(x−2)(3x - 1)(x + 4)(x - 2)(3x−1)(x+4)(x−2)

(x−4)(x+5)2(x - 4)(x + 5)^2(x−4)(x+5)2

(2x+1)(x−3)(x+4)(2x + 1)(x - 3)(x + 4)(2x+1)(x−3)(x+4)

(x−6)(x+2)2(x - 6)(x + 2)^2(x−6)(x+2)2

(x+3)(x−1)(x+5)(x + 3)(x - 1)(x + 5)(x+3)(x−1)(x+5)

(4x−2)(x+3)(x−5)(4x - 2)(x + 3)(x - 5)(4x−2)(x+3)(x−5)

Let's expand each of the given expressions step by step.

### 1. Expand \((x - 5)(x + 2)(x - 1)\)

#### Step 1: Expand the first two factors
\[
(x - 5)(x + 2) = x(x + 2) - 5(x + 2) = x^2 + 2x - 5x - 10 = x^2 - 3x - 10
\]

#### Step 2: Multiply by the third factor
\[
(x^2 - 3x - 10)(x - 1) = x^2(x - 1) - 3x(x - 1) - 10(x - 1)
\]
\[
= x^3 - x^2 - 3x^2 + 3x - 10x + 10 = x^3 - 4x^2 - 7x + 10
\]

So, the expanded form is:
\[
\boxed{x^3 - 4x^2 - 7x + 10}
\]

### 2. Expand \((2x + 3)(x - 4)(x + 5)\)

#### Step 1: Expand the first two factors
\[
(2x + 3)(x - 4) = 2x(x - 4) + 3(x - 4) = 2x^2 - 8x + 3x - 12 = 2x^2 - 5x - 12
\]

#### Step 2: Multiply by the third factor
\[
(2x^2 - 5x - 12)(x + 5) = 2x^2(x + 5) - 5x(x + 5) - 12(x + 5)
\]
\[
= 2x^3 + 10x^2 - 5x^2 - 25x - 12x - 60 = 2x^3 + 5x^2 - 37x - 60
\]

So, the expanded form is:
\[
\boxed{2x^3 + 5x^2 - 37x - 60}
\]

### 3. Expand \((x + 6)(x - 2)(x + 3)\)

#### Step 1: Expand the first two factors
\[
(x + 6)(x - 2) = x(x - 2) + 6(x - 2) = x^2 - 2x + 6x - 12 = x^2 + 4x - 12
\]

#### Step 2: Multiply by the third factor
\[
(x^2 + 4x - 12)(x + 3) = x^2(x + 3) + 4x(x + 3) - 12(x + 3)
\]
\[
= x^3 + 3x^2 + 4x^2 + 12x - 12x - 36 = x^3 + 7x^2 - 36
\]

So, the expanded form is:
\[
\boxed{x^3 + 7x^2 - 36}
\]

### 4. Expand \((3x - 1)(x + 4)(x - 2)\)

#### Step 1: Expand the first two factors
\[
(3x - 1)(x + 4) = 3x(x + 4) - 1(x + 4) = 3x^2 + 12x - x - 4 = 3x^2 + 11x - 4
\]

#### Step 2: Multiply by the third factor
\[
(3x^2 + 11x - 4)(x - 2) = 3x^2(x - 2) + 11x(x - 2) - 4(x - 2)
\]
\[
= 3x^3 - 6x^2 + 11x^2 - 22x - 4x + 8 = 3x^3 + 5x^2 - 26x + 8
\]

So, the expanded form is:
\[
\boxed{3x^3 + 5x^2 - 26x + 8}
\]

### 5. Expand \((x - 4)(x + 5)^2\)

#### Step 1: Expand \((x + 5)^2\)
\[
(x + 5)^2 = (x + 5)(x + 5) = x^2 + 5x + 5x + 25 = x^2 + 10x + 25
\]

#### Step 2: Multiply by \((x - 4)\)
\[
(x - 4)(x^2 + 10x + 25) = x(x^2 + 10x + 25) - 4(x^2 + 10x + 25)
\]
\[
= x^3 + 10x^2 + 25x - 4x^2 - 40x - 100 = x^3 + 6x^2 - 15x - 100
\]

So, the expanded form is:
\[
\boxed{x^3 + 6x^2 - 15x - 100}
\]

### 6. Expand \((2x + 1)(x - 3)(x + 4)\)

#### Step 1: Expand the first two factors
\[
(2x + 1)(x - 3) = 2x(x - 3) + 1(x - 3) = 2x^2 - 6x + x - 3 = 2x^2 - 5x - 3
\]

#### Step 2: Multiply by the third factor
\[
(2x^2 - 5x - 3)(x + 4) = 2x^2(x + 4) - 5x(x + 4) - 3(x + 4)
\]
\[
= 2x^3 + 8x^2 - 5x^2 - 20x - 3x - 12 = 2x^3 + 3x^2 - 23x - 12
\]

So, the expanded form is:
\[
\boxed{2x^3 + 3x^2 - 23x - 12}
\]

### 7. Expand \((x - 6)(x + 2)^2\)

#### Step 1: Expand \((x + 2)^2\)
\[
(x + 2)^2 = (x + 2)(x + 2) = x^2 + 2x + 2x + 4 = x^2 + 4x + 4
\]

#### Step 2: Multiply by \((x - 6)\)
\[
(x - 6)(x^2 + 4x + 4) = x(x^2 + 4x + 4) - 6(x^2 + 4x + 4)
\]
\[
= x^3 + 4x^2 + 4x - 6x^2 - 24x - 24 = x^3 - 2x^2 - 20x - 24
\]

So, the expanded form is:
\[
\boxed{x^3 - 2x^

Learn how to expand the polynomial (x−5)(x+2)(x−1) step-by-step with detailed solutions. This problem covers polynomial multiplication using the distributive property. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation