Find the Product (4-5x)(1-2x)(3x+2)

$(4 - 5 x) (1 - 2 x) (3 x + 2)$

Step 1

Expand $(4 - 5 x) (1 - 2 x)$ using the FOIL Method.

Apply the distributive property.

$(4 (1 - 2 x) - 5 x (1 - 2 x)) (3 x + 2)$

Apply the distributive property.

$(4 \cdot 1 + 4 (- 2 x) - 5 x (1 - 2 x)) (3 x + 2)$

Apply the distributive property.

$(4 \cdot 1 + 4 (- 2 x) - 5 x \cdot 1 - 5 x (- 2 x)) (3 x + 2)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $1$ .

$(4 + 4 (- 2 x) - 5 x \cdot 1 - 5 x (- 2 x)) (3 x + 2)$

Multiply $- 2$ by $4$ .

$(4 - 8 x - 5 x \cdot 1 - 5 x (- 2 x)) (3 x + 2)$

Multiply $- 5$ by $1$ .

$(4 - 8 x - 5 x - 5 x (- 2 x)) (3 x + 2)$

Rewrite using the commutative property of multiplication.

$(4 - 8 x - 5 x - 5 \cdot - 2 x \cdot x) (3 x + 2)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$(4 - 8 x - 5 x - 5 \cdot - 2 (x \cdot x)) (3 x + 2)$

Multiply $x$ by $x$ .

$(4 - 8 x - 5 x - 5 \cdot - 2 x^{2}) (3 x + 2)$

Multiply $- 5$ by $- 2$ .

$(4 - 8 x - 5 x + 10 x^{2}) (3 x + 2)$

Subtract $5 x$ from $- 8 x$ .

$(4 - 13 x + 10 x^{2}) (3 x + 2)$

Step 3

Expand $(4 - 13 x + 10 x^{2}) (3 x + 2)$ by multiplying each term in the first expression by each term in the second expression.

$4 (3 x) + 4 \cdot 2 - 13 x (3 x) - 13 x \cdot 2 + 10 x^{2} (3 x) + 10 x^{2} \cdot 2$

Step 4

Simplify terms.

Simplify each term.

Multiply $3$ by $4$ .

$12 x + 4 \cdot 2 - 13 x (3 x) - 13 x \cdot 2 + 10 x^{2} (3 x) + 10 x^{2} \cdot 2$

Multiply $4$ by $2$ .

$12 x + 8 - 13 x (3 x) - 13 x \cdot 2 + 10 x^{2} (3 x) + 10 x^{2} \cdot 2$

Rewrite using the commutative property of multiplication.

$12 x + 8 - 13 \cdot 3 x \cdot x - 13 x \cdot 2 + 10 x^{2} (3 x) + 10 x^{2} \cdot 2$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$12 x + 8 - 13 \cdot 3 (x \cdot x) - 13 x \cdot 2 + 10 x^{2} (3 x) + 10 x^{2} \cdot 2$

Multiply $x$ by $x$ .

$12 x + 8 - 13 \cdot 3 x^{2} - 13 x \cdot 2 + 10 x^{2} (3 x) + 10 x^{2} \cdot 2$

Multiply $- 13$ by $3$ .

$12 x + 8 - 39 x^{2} - 13 x \cdot 2 + 10 x^{2} (3 x) + 10 x^{2} \cdot 2$

Multiply $2$ by $- 13$ .

$12 x + 8 - 39 x^{2} - 26 x + 10 x^{2} (3 x) + 10 x^{2} \cdot 2$

Rewrite using the commutative property of multiplication.

$12 x + 8 - 39 x^{2} - 26 x + 10 \cdot 3 x^{2} x + 10 x^{2} \cdot 2$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$12 x + 8 - 39 x^{2} - 26 x + 10 \cdot 3 (x \cdot x^{2}) + 10 x^{2} \cdot 2$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$12 x + 8 - 39 x^{2} - 26 x + 10 \cdot 3 (x^{1} x^{2}) + 10 x^{2} \cdot 2$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 x + 8 - 39 x^{2} - 26 x + 10 \cdot 3 x^{1 + 2} + 10 x^{2} \cdot 2$

Add $1$ and $2$ .

$12 x + 8 - 39 x^{2} - 26 x + 10 \cdot 3 x^{3} + 10 x^{2} \cdot 2$

Multiply $10$ by $3$ .

$12 x + 8 - 39 x^{2} - 26 x + 30 x^{3} + 10 x^{2} \cdot 2$

Multiply $2$ by $10$ .

$12 x + 8 - 39 x^{2} - 26 x + 30 x^{3} + 20 x^{2}$

Simplify by adding terms.

Subtract $26 x$ from $12 x$ .

$- 14 x + 8 - 39 x^{2} + 30 x^{3} + 20 x^{2}$

Add $- 39 x^{2}$ and $20 x^{2}$ .

$- 14 x + 8 + 30 x^{3} - 19 x^{2}$

Find the Product (4-5x)(1-2x)(3x+2)

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