Simplify 4p^2(5p^2+7p-6)-4p^2(8p^2-9p-10)

$4 p^{2} (5 p^{2} + 7 p - 6) - 4 p^{2} (8 p^{2} - 9 p - 10)$

Simplify each term.

Apply the distributive property.

$4 p^{2} (5 p^{2}) + 4 p^{2} (7 p) + 4 p^{2} \cdot - 6 - 4 p^{2} (8 p^{2} - 9 p - 10)$

Simplify.

Rewrite using the commutative property of multiplication.

$4 \cdot 5 p^{2} p^{2} + 4 p^{2} (7 p) + 4 p^{2} \cdot - 6 - 4 p^{2} (8 p^{2} - 9 p - 10)$

Rewrite using the commutative property of multiplication.

$4 \cdot 5 p^{2} p^{2} + 4 \cdot 7 p^{2} p + 4 p^{2} \cdot - 6 - 4 p^{2} (8 p^{2} - 9 p - 10)$

Multiply $- 6$ by $4$ .

$4 \cdot 5 p^{2} p^{2} + 4 \cdot 7 p^{2} p - 24 p^{2} - 4 p^{2} (8 p^{2} - 9 p - 10)$

Simplify each term.

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

Move $p^{2}$ .

$4 \cdot 5 (p^{2} p^{2}) + 4 \cdot 7 p^{2} p - 24 p^{2} - 4 p^{2} (8 p^{2} - 9 p - 10)$

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

$4 \cdot 5 p^{2 + 2} + 4 \cdot 7 p^{2} p - 24 p^{2} - 4 p^{2} (8 p^{2} - 9 p - 10)$

Add $2$ and $2$ .

$4 \cdot 5 p^{4} + 4 \cdot 7 p^{2} p - 24 p^{2} - 4 p^{2} (8 p^{2} - 9 p - 10)$

Multiply $4$ by $5$ .

$20 p^{4} + 4 \cdot 7 p^{2} p - 24 p^{2} - 4 p^{2} (8 p^{2} - 9 p - 10)$

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

Move $p$ .

$20 p^{4} + 4 \cdot 7 (p \cdot p^{2}) - 24 p^{2} - 4 p^{2} (8 p^{2} - 9 p - 10)$

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

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

$20 p^{4} + 4 \cdot 7 (p^{1} p^{2}) - 24 p^{2} - 4 p^{2} (8 p^{2} - 9 p - 10)$

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

$20 p^{4} + 4 \cdot 7 p^{1 + 2} - 24 p^{2} - 4 p^{2} (8 p^{2} - 9 p - 10)$

Add $1$ and $2$ .

$20 p^{4} + 4 \cdot 7 p^{3} - 24 p^{2} - 4 p^{2} (8 p^{2} - 9 p - 10)$

Multiply $4$ by $7$ .

$20 p^{4} + 28 p^{3} - 24 p^{2} - 4 p^{2} (8 p^{2} - 9 p - 10)$

Apply the distributive property.

$20 p^{4} + 28 p^{3} - 24 p^{2} - 4 p^{2} (8 p^{2}) - 4 p^{2} (- 9 p) - 4 p^{2} \cdot - 10$

Simplify.

Rewrite using the commutative property of multiplication.

$20 p^{4} + 28 p^{3} - 24 p^{2} - 4 \cdot 8 p^{2} p^{2} - 4 p^{2} (- 9 p) - 4 p^{2} \cdot - 10$

Rewrite using the commutative property of multiplication.

$20 p^{4} + 28 p^{3} - 24 p^{2} - 4 \cdot 8 p^{2} p^{2} - 4 \cdot - 9 p^{2} p - 4 p^{2} \cdot - 10$

Multiply $- 10$ by $- 4$ .

$20 p^{4} + 28 p^{3} - 24 p^{2} - 4 \cdot 8 p^{2} p^{2} - 4 \cdot - 9 p^{2} p + 40 p^{2}$

Simplify each term.

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

Move $p^{2}$ .

$20 p^{4} + 28 p^{3} - 24 p^{2} - 4 \cdot 8 (p^{2} p^{2}) - 4 \cdot - 9 p^{2} p + 40 p^{2}$

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

$20 p^{4} + 28 p^{3} - 24 p^{2} - 4 \cdot 8 p^{2 + 2} - 4 \cdot - 9 p^{2} p + 40 p^{2}$

Add $2$ and $2$ .

$20 p^{4} + 28 p^{3} - 24 p^{2} - 4 \cdot 8 p^{4} - 4 \cdot - 9 p^{2} p + 40 p^{2}$

Multiply $- 4$ by $8$ .

$20 p^{4} + 28 p^{3} - 24 p^{2} - 32 p^{4} - 4 \cdot - 9 p^{2} p + 40 p^{2}$

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

Move $p$ .

$20 p^{4} + 28 p^{3} - 24 p^{2} - 32 p^{4} - 4 \cdot - 9 (p \cdot p^{2}) + 40 p^{2}$

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

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

$20 p^{4} + 28 p^{3} - 24 p^{2} - 32 p^{4} - 4 \cdot - 9 (p^{1} p^{2}) + 40 p^{2}$

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

$20 p^{4} + 28 p^{3} - 24 p^{2} - 32 p^{4} - 4 \cdot - 9 p^{1 + 2} + 40 p^{2}$

Add $1$ and $2$ .

$20 p^{4} + 28 p^{3} - 24 p^{2} - 32 p^{4} - 4 \cdot - 9 p^{3} + 40 p^{2}$

Multiply $- 4$ by $- 9$ .

$20 p^{4} + 28 p^{3} - 24 p^{2} - 32 p^{4} + 36 p^{3} + 40 p^{2}$

Simplify by adding terms.

Subtract $32 p^{4}$ from $20 p^{4}$ .

$- 12 p^{4} + 28 p^{3} - 24 p^{2} + 36 p^{3} + 40 p^{2}$

Add $28 p^{3}$ and $36 p^{3}$ .

$- 12 p^{4} + 64 p^{3} - 24 p^{2} + 40 p^{2}$

Add $- 24 p^{2}$ and $40 p^{2}$ .

$- 12 p^{4} + 64 p^{3} + 16 p^{2}$

Simplify 4p^2(5p^2+7p-6)-4p^2(8p^2-9p-10)

Related Questions

Support LCMGCF.com by disabling your adblocker.