Simplify (2x^2+6x-4)(2x^2-3x)

$(2 x^{2} + 6 x - 4) (2 x^{2} - 3 x)$

Step 1

Expand $(2 x^{2} + 6 x - 4) (2 x^{2} - 3 x)$ by multiplying each term in the first expression by each term in the second expression.

$2 x^{2} (2 x^{2}) + 2 x^{2} (- 3 x) + 6 x (2 x^{2}) + 6 x (- 3 x) - 4 (2 x^{2}) - 4 (- 3 x)$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $2$ by $2$ .

$4 x^{4} + 2 x^{2} (- 3 x) + 6 x (2 x^{2}) + 6 x (- 3 x) - 4 (2 x^{2}) - 4 (- 3 x)$

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $- 3$ .

$4 x^{4} - 6 x^{3} + 6 x (2 x^{2}) + 6 x (- 3 x) - 4 (2 x^{2}) - 4 (- 3 x)$

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $6$ by $2$ .

$4 x^{4} - 6 x^{3} + 12 x^{3} + 6 x (- 3 x) - 4 (2 x^{2}) - 4 (- 3 x)$

Rewrite using the commutative property of multiplication.

$4 x^{4} - 6 x^{3} + 12 x^{3} + 6 \cdot - 3 x \cdot x - 4 (2 x^{2}) - 4 (- 3 x)$

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

Move $x$ .

$4 x^{4} - 6 x^{3} + 12 x^{3} + 6 \cdot - 3 (x \cdot x) - 4 (2 x^{2}) - 4 (- 3 x)$

Multiply $x$ by $x$ .

$4 x^{4} - 6 x^{3} + 12 x^{3} + 6 \cdot - 3 x^{2} - 4 (2 x^{2}) - 4 (- 3 x)$

Multiply $6$ by $- 3$ .

$4 x^{4} - 6 x^{3} + 12 x^{3} - 18 x^{2} - 4 (2 x^{2}) - 4 (- 3 x)$

Multiply $2$ by $- 4$ .

$4 x^{4} - 6 x^{3} + 12 x^{3} - 18 x^{2} - 8 x^{2} - 4 (- 3 x)$

Multiply $- 3$ by $- 4$ .

$4 x^{4} - 6 x^{3} + 12 x^{3} - 18 x^{2} - 8 x^{2} + 12 x$

Simplify by adding terms.

Add $- 6 x^{3}$ and $12 x^{3}$ .

$4 x^{4} + 6 x^{3} - 18 x^{2} - 8 x^{2} + 12 x$

Subtract $8 x^{2}$ from $- 18 x^{2}$ .

$4 x^{4} + 6 x^{3} - 26 x^{2} + 12 x$

Simplify (2x^2+6x-4)(2x^2-3x)

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