Simplify (m^2-7m-6)(7m^2-3m-7)

$(m^{2} - 7 m - 6) (7 m^{2} - 3 m - 7)$

Step 1

Expand $(m^{2} - 7 m - 6) (7 m^{2} - 3 m - 7)$ by multiplying each term in the first expression by each term in the second expression.

$m^{2} (7 m^{2}) + m^{2} (- 3 m) + m^{2} \cdot - 7 - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 m^{2} m^{2} + m^{2} (- 3 m) + m^{2} \cdot - 7 - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

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

Move $m^{2}$ .

$7 (m^{2} m^{2}) + m^{2} (- 3 m) + m^{2} \cdot - 7 - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

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

$7 m^{2 + 2} + m^{2} (- 3 m) + m^{2} \cdot - 7 - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Add $2$ and $2$ .

$7 m^{4} + m^{2} (- 3 m) + m^{2} \cdot - 7 - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Rewrite using the commutative property of multiplication.

$7 m^{4} - 3 m^{2} m + m^{2} \cdot - 7 - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

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

Move $m$ .

$7 m^{4} - 3 (m \cdot m^{2}) + m^{2} \cdot - 7 - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

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

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

$7 m^{4} - 3 (m^{1} m^{2}) + m^{2} \cdot - 7 - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

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

$7 m^{4} - 3 m^{1 + 2} + m^{2} \cdot - 7 - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Add $1$ and $2$ .

$7 m^{4} - 3 m^{3} + m^{2} \cdot - 7 - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Move $- 7$ to the left of $m^{2}$ .

$7 m^{4} - 3 m^{3} - 7 \cdot m^{2} - 7 m (7 m^{2}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Rewrite using the commutative property of multiplication.

$7 m^{4} - 3 m^{3} - 7 m^{2} - 7 \cdot 7 m \cdot m^{2} - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

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

Move $m^{2}$ .

$7 m^{4} - 3 m^{3} - 7 m^{2} - 7 \cdot 7 (m^{2} m) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

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

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

$7 m^{4} - 3 m^{3} - 7 m^{2} - 7 \cdot 7 (m^{2} m^{1}) - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

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

$7 m^{4} - 3 m^{3} - 7 m^{2} - 7 \cdot 7 m^{2 + 1} - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Add $2$ and $1$ .

$7 m^{4} - 3 m^{3} - 7 m^{2} - 7 \cdot 7 m^{3} - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Multiply $- 7$ by $7$ .

$7 m^{4} - 3 m^{3} - 7 m^{2} - 49 m^{3} - 7 m (- 3 m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Rewrite using the commutative property of multiplication.

$7 m^{4} - 3 m^{3} - 7 m^{2} - 49 m^{3} - 7 \cdot - 3 m \cdot m - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$7 m^{4} - 3 m^{3} - 7 m^{2} - 49 m^{3} - 7 \cdot - 3 (m \cdot m) - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Multiply $m$ by $m$ .

$7 m^{4} - 3 m^{3} - 7 m^{2} - 49 m^{3} - 7 \cdot - 3 m^{2} - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Multiply $- 7$ by $- 3$ .

$7 m^{4} - 3 m^{3} - 7 m^{2} - 49 m^{3} + 21 m^{2} - 7 m \cdot - 7 - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$7 m^{4} - 3 m^{3} - 7 m^{2} - 49 m^{3} + 21 m^{2} + 49 m - 6 (7 m^{2}) - 6 (- 3 m) - 6 \cdot - 7$

Multiply $7$ by $- 6$ .

$7 m^{4} - 3 m^{3} - 7 m^{2} - 49 m^{3} + 21 m^{2} + 49 m - 42 m^{2} - 6 (- 3 m) - 6 \cdot - 7$

Multiply $- 3$ by $- 6$ .

$7 m^{4} - 3 m^{3} - 7 m^{2} - 49 m^{3} + 21 m^{2} + 49 m - 42 m^{2} + 18 m - 6 \cdot - 7$

Multiply $- 6$ by $- 7$ .

$7 m^{4} - 3 m^{3} - 7 m^{2} - 49 m^{3} + 21 m^{2} + 49 m - 42 m^{2} + 18 m + 42$

Simplify by adding terms.

Subtract $49 m^{3}$ from $- 3 m^{3}$ .

$7 m^{4} - 52 m^{3} - 7 m^{2} + 21 m^{2} + 49 m - 42 m^{2} + 18 m + 42$

Add $- 7 m^{2}$ and $21 m^{2}$ .

$7 m^{4} - 52 m^{3} + 14 m^{2} + 49 m - 42 m^{2} + 18 m + 42$

Subtract $42 m^{2}$ from $14 m^{2}$ .

$7 m^{4} - 52 m^{3} - 28 m^{2} + 49 m + 18 m + 42$

Add $49 m$ and $18 m$ .

$7 m^{4} - 52 m^{3} - 28 m^{2} + 67 m + 42$

Simplify (m^2-7m-6)(7m^2-3m-7)

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