Write in Standard Form (x^2+2x-3)(3x^2-2x+4)

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

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

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

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Move $4$ to the left of $x^{2}$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $- 2$ .

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

Multiply $4$ by $2$ .

$3 x^{4} - 2 x^{3} + 4 x^{2} + 6 x^{3} - 4 x^{2} + 8 x - 3 (3 x^{2}) - 3 (- 2 x) - 3 \cdot 4$

Multiply $3$ by $- 3$ .

$3 x^{4} - 2 x^{3} + 4 x^{2} + 6 x^{3} - 4 x^{2} + 8 x - 9 x^{2} - 3 (- 2 x) - 3 \cdot 4$

Multiply $- 2$ by $- 3$ .

$3 x^{4} - 2 x^{3} + 4 x^{2} + 6 x^{3} - 4 x^{2} + 8 x - 9 x^{2} + 6 x - 3 \cdot 4$

Multiply $- 3$ by $4$ .

$3 x^{4} - 2 x^{3} + 4 x^{2} + 6 x^{3} - 4 x^{2} + 8 x - 9 x^{2} + 6 x - 12$

Simplify by adding terms.

Combine the opposite terms in $3 x^{4} - 2 x^{3} + 4 x^{2} + 6 x^{3} - 4 x^{2} + 8 x - 9 x^{2} + 6 x - 12$ .

Subtract $4 x^{2}$ from $4 x^{2}$ .

$3 x^{4} - 2 x^{3} + 6 x^{3} + 0 + 8 x - 9 x^{2} + 6 x - 12$

Add $3 x^{4} - 2 x^{3} + 6 x^{3}$ and $0$ .

$3 x^{4} - 2 x^{3} + 6 x^{3} + 8 x - 9 x^{2} + 6 x - 12$

Add $- 2 x^{3}$ and $6 x^{3}$ .

$3 x^{4} + 4 x^{3} + 8 x - 9 x^{2} + 6 x - 12$

Add $8 x$ and $6 x$ .

$3 x^{4} + 4 x^{3} - 9 x^{2} + 14 x - 12$

Write in Standard Form (x^2+2x-3)(3x^2-2x+4)

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