Simplify (6x^2-6x-5)(7x^2+6x-5)

$(6 x^{2} - 6 x - 5) (7 x^{2} + 6 x - 5)$

Step 1

Expand $(6 x^{2} - 6 x - 5) (7 x^{2} + 6 x - 5)$ by multiplying each term in the first expression by each term in the second expression.

$6 x^{2} (7 x^{2}) + 6 x^{2} (6 x) + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$6 \cdot 7 x^{2} x^{2} + 6 x^{2} (6 x) + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

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

Move $x^{2}$ .

$6 \cdot 7 (x^{2} x^{2}) + 6 x^{2} (6 x) + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

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

$6 \cdot 7 x^{2 + 2} + 6 x^{2} (6 x) + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Add $2$ and $2$ .

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

Multiply $6$ by $7$ .

$42 x^{4} + 6 x^{2} (6 x) + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Rewrite using the commutative property of multiplication.

$42 x^{4} + 6 \cdot 6 x^{2} x + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

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

Move $x$ .

$42 x^{4} + 6 \cdot 6 (x \cdot x^{2}) + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

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

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

$42 x^{4} + 6 \cdot 6 (x^{1} x^{2}) + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

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

$42 x^{4} + 6 \cdot 6 x^{1 + 2} + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Add $1$ and $2$ .

$42 x^{4} + 6 \cdot 6 x^{3} + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Multiply $6$ by $6$ .

$42 x^{4} + 36 x^{3} + 6 x^{2} \cdot - 5 - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Multiply $- 5$ by $6$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 6 x (7 x^{2}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Rewrite using the commutative property of multiplication.

$42 x^{4} + 36 x^{3} - 30 x^{2} - 6 \cdot 7 x \cdot x^{2} - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

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

Move $x^{2}$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 6 \cdot 7 (x^{2} x) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

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

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

$42 x^{4} + 36 x^{3} - 30 x^{2} - 6 \cdot 7 (x^{2} x^{1}) - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

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

$42 x^{4} + 36 x^{3} - 30 x^{2} - 6 \cdot 7 x^{2 + 1} - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Add $2$ and $1$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 6 \cdot 7 x^{3} - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Multiply $- 6$ by $7$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 6 x (6 x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Rewrite using the commutative property of multiplication.

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 6 \cdot 6 x \cdot x - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

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

Move $x$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 6 \cdot 6 (x \cdot x) - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Multiply $x$ by $x$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 6 \cdot 6 x^{2} - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Multiply $- 6$ by $6$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 36 x^{2} - 6 x \cdot - 5 - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Multiply $- 5$ by $- 6$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 36 x^{2} + 30 x - 5 (7 x^{2}) - 5 (6 x) - 5 \cdot - 5$

Multiply $7$ by $- 5$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 36 x^{2} + 30 x - 35 x^{2} - 5 (6 x) - 5 \cdot - 5$

Multiply $6$ by $- 5$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 36 x^{2} + 30 x - 35 x^{2} - 30 x - 5 \cdot - 5$

Multiply $- 5$ by $- 5$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 36 x^{2} + 30 x - 35 x^{2} - 30 x + 25$

Simplify by adding terms.

Combine the opposite terms in $42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 36 x^{2} + 30 x - 35 x^{2} - 30 x + 25$ .

Subtract $30 x$ from $30 x$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 36 x^{2} - 35 x^{2} + 0 + 25$

Add $42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 36 x^{2} - 35 x^{2}$ and $0$ .

$42 x^{4} + 36 x^{3} - 30 x^{2} - 42 x^{3} - 36 x^{2} - 35 x^{2} + 25$

Subtract $42 x^{3}$ from $36 x^{3}$ .

$42 x^{4} - 6 x^{3} - 30 x^{2} - 36 x^{2} - 35 x^{2} + 25$

Subtract $36 x^{2}$ from $- 30 x^{2}$ .

$42 x^{4} - 6 x^{3} - 66 x^{2} - 35 x^{2} + 25$

Subtract $35 x^{2}$ from $- 66 x^{2}$ .

$42 x^{4} - 6 x^{3} - 101 x^{2} + 25$

Simplify (6x^2-6x-5)(7x^2+6x-5)

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