Find the Product (7x^2)(2x^3+5)(x^2-4x-9)

$(7 x^{2}) (2 x^{3} + 5) (x^{2} - 4 x - 9)$

Step 1

Simplify terms.

Apply the distributive property.

$(7 x^{2} (2 x^{3}) + 7 x^{2} \cdot 5) (x^{2} - 4 x - 9)$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$(7 \cdot 2 x^{2} x^{3} + 7 x^{2} \cdot 5) (x^{2} - 4 x - 9)$

Multiply $5$ by $7$ .

$(7 \cdot 2 x^{2} x^{3} + 35 x^{2}) (x^{2} - 4 x - 9)$

Simplify each term.

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$(7 \cdot 2 (x^{3} x^{2}) + 35 x^{2}) (x^{2} - 4 x - 9)$

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

$(7 \cdot 2 x^{3 + 2} + 35 x^{2}) (x^{2} - 4 x - 9)$

Add $3$ and $2$ .

$(7 \cdot 2 x^{5} + 35 x^{2}) (x^{2} - 4 x - 9)$

Multiply $7$ by $2$ .

$(14 x^{5} + 35 x^{2}) (x^{2} - 4 x - 9)$

Step 2

Expand $(14 x^{5} + 35 x^{2}) (x^{2} - 4 x - 9)$ by multiplying each term in the first expression by each term in the second expression.

$14 x^{5} x^{2} + 14 x^{5} (- 4 x) + 14 x^{5} \cdot - 9 + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

Step 3

Simplify each term.

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$14 (x^{2} x^{5}) + 14 x^{5} (- 4 x) + 14 x^{5} \cdot - 9 + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

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

$14 x^{2 + 5} + 14 x^{5} (- 4 x) + 14 x^{5} \cdot - 9 + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

Add $2$ and $5$ .

$14 x^{7} + 14 x^{5} (- 4 x) + 14 x^{5} \cdot - 9 + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

Rewrite using the commutative property of multiplication.

$14 x^{7} + 14 \cdot - 4 x^{5} x + 14 x^{5} \cdot - 9 + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

Multiply $x^{5}$ by $x$ by adding the exponents.

Move $x$ .

$14 x^{7} + 14 \cdot - 4 (x \cdot x^{5}) + 14 x^{5} \cdot - 9 + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

Multiply $x$ by $x^{5}$ .

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

$14 x^{7} + 14 \cdot - 4 (x^{1} x^{5}) + 14 x^{5} \cdot - 9 + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

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

$14 x^{7} + 14 \cdot - 4 x^{1 + 5} + 14 x^{5} \cdot - 9 + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

Add $1$ and $5$ .

$14 x^{7} + 14 \cdot - 4 x^{6} + 14 x^{5} \cdot - 9 + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

Multiply $14$ by $- 4$ .

$14 x^{7} - 56 x^{6} + 14 x^{5} \cdot - 9 + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

Multiply $- 9$ by $14$ .

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 x^{2} x^{2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

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

Move $x^{2}$ .

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 (x^{2} x^{2}) + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

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

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 x^{2 + 2} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

Add $2$ and $2$ .

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 x^{4} + 35 x^{2} (- 4 x) + 35 x^{2} \cdot - 9$

Rewrite using the commutative property of multiplication.

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 x^{4} + 35 \cdot - 4 x^{2} x + 35 x^{2} \cdot - 9$

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

Move $x$ .

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 x^{4} + 35 \cdot - 4 (x \cdot x^{2}) + 35 x^{2} \cdot - 9$

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

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

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 x^{4} + 35 \cdot - 4 (x^{1} x^{2}) + 35 x^{2} \cdot - 9$

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

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 x^{4} + 35 \cdot - 4 x^{1 + 2} + 35 x^{2} \cdot - 9$

Add $1$ and $2$ .

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 x^{4} + 35 \cdot - 4 x^{3} + 35 x^{2} \cdot - 9$

Multiply $35$ by $- 4$ .

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 x^{4} - 140 x^{3} + 35 x^{2} \cdot - 9$

Multiply $- 9$ by $35$ .

$14 x^{7} - 56 x^{6} - 126 x^{5} + 35 x^{4} - 140 x^{3} - 315 x^{2}$

Find the Product (7x^2)(2x^3+5)(x^2-4x-9)

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