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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $2$ .

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

Multiply $5$ by $- 2$ .

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

Add $- 4 x$ and $5 x$ .

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

Step 3

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

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

Step 4

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

$2 \cdot 3 (x^{1} x^{2}) + 2 x^{2} \cdot 4 + x (3 x) + x \cdot 4 - 10 (3 x) - 10 \cdot 4$

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

$2 \cdot 3 x^{1 + 2} + 2 x^{2} \cdot 4 + x (3 x) + x \cdot 4 - 10 (3 x) - 10 \cdot 4$

Add $1$ and $2$ .

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

Multiply $2$ by $3$ .

$6 x^{3} + 2 x^{2} \cdot 4 + x (3 x) + x \cdot 4 - 10 (3 x) - 10 \cdot 4$

Multiply $4$ by $2$ .

$6 x^{3} + 8 x^{2} + x (3 x) + x \cdot 4 - 10 (3 x) - 10 \cdot 4$

Rewrite using the commutative property of multiplication.

$6 x^{3} + 8 x^{2} + 3 x \cdot x + x \cdot 4 - 10 (3 x) - 10 \cdot 4$

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

Move $x$ .

$6 x^{3} + 8 x^{2} + 3 (x \cdot x) + x \cdot 4 - 10 (3 x) - 10 \cdot 4$

Multiply $x$ by $x$ .

$6 x^{3} + 8 x^{2} + 3 x^{2} + x \cdot 4 - 10 (3 x) - 10 \cdot 4$

Move $4$ to the left of $x$ .

$6 x^{3} + 8 x^{2} + 3 x^{2} + 4 \cdot x - 10 (3 x) - 10 \cdot 4$

Multiply $3$ by $- 10$ .

$6 x^{3} + 8 x^{2} + 3 x^{2} + 4 x - 30 x - 10 \cdot 4$

Multiply $- 10$ by $4$ .

$6 x^{3} + 8 x^{2} + 3 x^{2} + 4 x - 30 x - 40$

Simplify by adding terms.

Add $8 x^{2}$ and $3 x^{2}$ .

$6 x^{3} + 11 x^{2} + 4 x - 30 x - 40$

Subtract $30 x$ from $4 x$ .

$6 x^{3} + 11 x^{2} - 26 x - 40$

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

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