Simplify -1.4p^2x^6*(5p^3x-1.5px^2-2x^3)

$- 1.4 p^{2} x^{6} \cdot (5 p^{3} x - 1.5 p x^{2} - 2 x^{3})$

Step 1

Apply the distributive property.

$- 1.4 p^{2} x^{6} (5 p^{3} x) - 1.4 p^{2} x^{6} (- 1.5 p x^{2}) - 1.4 p^{2} x^{6} (- 2 x^{3})$

Step 2

Simplify.

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

Move $p^{3}$ .

$- 1.4 (p^{3} p^{2}) x^{6} (5 x) - 1.4 p^{2} x^{6} (- 1.5 p x^{2}) - 1.4 p^{2} x^{6} (- 2 x^{3})$

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

$- 1.4 p^{3 + 2} x^{6} (5 x) - 1.4 p^{2} x^{6} (- 1.5 p x^{2}) - 1.4 p^{2} x^{6} (- 2 x^{3})$

Add $3$ and $2$ .

$- 1.4 p^{5} x^{6} (5 x) - 1.4 p^{2} x^{6} (- 1.5 p x^{2}) - 1.4 p^{2} x^{6} (- 2 x^{3})$

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

Move $p$ .

$- 1.4 p^{5} x^{6} (5 x) - 1.4 (p \cdot p^{2}) x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{6} (- 2 x^{3})$

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

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

$- 1.4 p^{5} x^{6} (5 x) - 1.4 (p^{1} p^{2}) x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{6} (- 2 x^{3})$

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

$- 1.4 p^{5} x^{6} (5 x) - 1.4 p^{1 + 2} x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{6} (- 2 x^{3})$

Add $1$ and $2$ .

$- 1.4 p^{5} x^{6} (5 x) - 1.4 p^{3} x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{6} (- 2 x^{3})$

Multiply $x^{6}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$- 1.4 p^{5} x^{6} (5 x) - 1.4 p^{3} x^{6} (- 1.5 x^{2}) - 1.4 p^{2} (x^{3} x^{6}) \cdot - 2$

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

$- 1.4 p^{5} x^{6} (5 x) - 1.4 p^{3} x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{3 + 6} \cdot - 2$

Add $3$ and $6$ .

$- 1.4 p^{5} x^{6} (5 x) - 1.4 p^{3} x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{9} \cdot - 2$

Step 3

Simplify each term.

Multiply $x^{6}$ by $x$ by adding the exponents.

Move $x$ .

$- 1.4 p^{5} (x \cdot x^{6}) \cdot 5 - 1.4 p^{3} x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{9} \cdot - 2$

Multiply $x$ by $x^{6}$ .

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

$- 1.4 p^{5} (x^{1} x^{6}) \cdot 5 - 1.4 p^{3} x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{9} \cdot - 2$

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

$- 1.4 p^{5} x^{1 + 6} \cdot 5 - 1.4 p^{3} x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{9} \cdot - 2$

Add $1$ and $6$ .

$- 1.4 p^{5} x^{7} \cdot 5 - 1.4 p^{3} x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{9} \cdot - 2$

Multiply $5$ by $- 1.4$ .

$- 7 p^{5} x^{7} - 1.4 p^{3} x^{6} (- 1.5 x^{2}) - 1.4 p^{2} x^{9} \cdot - 2$

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$- 7 p^{5} x^{7} - 1.4 p^{3} (x^{2} x^{6}) \cdot - 1.5 - 1.4 p^{2} x^{9} \cdot - 2$

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

$- 7 p^{5} x^{7} - 1.4 p^{3} x^{2 + 6} \cdot - 1.5 - 1.4 p^{2} x^{9} \cdot - 2$

Add $2$ and $6$ .

$- 7 p^{5} x^{7} - 1.4 p^{3} x^{8} \cdot - 1.5 - 1.4 p^{2} x^{9} \cdot - 2$

Multiply $- 1.5$ by $- 1.4$ .

$- 7 p^{5} x^{7} + 2.1 p^{3} x^{8} - 1.4 p^{2} x^{9} \cdot - 2$

Multiply $- 2$ by $- 1.4$ .

$- 7 p^{5} x^{7} + 2.1 p^{3} x^{8} + 2.8 p^{2} x^{9}$

Simplify -1.4p^2x^6*(5p^3x-1.5px^2-2x^3)

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