Write in Standard Form (3x^2-x-5)(3x^2-3x+4)

$(3 x^{2} - x - 5) (3 x^{2} - 3 x + 4)$

Step 1

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

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

Step 2

Expand $(3 x^{2} - x - 5) (3 x^{2} - 3 x + 4)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 3

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $3$ by $3$ .

$9 x^{4} + 3 x^{2} (- 3 x) + 3 x^{2} \cdot 4 - x (3 x^{2}) - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Rewrite using the commutative property of multiplication.

$9 x^{4} + 3 \cdot - 3 x^{2} x + 3 x^{2} \cdot 4 - x (3 x^{2}) - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

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

Move $x$ .

$9 x^{4} + 3 \cdot - 3 (x \cdot x^{2}) + 3 x^{2} \cdot 4 - x (3 x^{2}) - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

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

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

$9 x^{4} + 3 \cdot - 3 (x^{1} x^{2}) + 3 x^{2} \cdot 4 - x (3 x^{2}) - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

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

$9 x^{4} + 3 \cdot - 3 x^{1 + 2} + 3 x^{2} \cdot 4 - x (3 x^{2}) - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Add $1$ and $2$ .

$9 x^{4} + 3 \cdot - 3 x^{3} + 3 x^{2} \cdot 4 - x (3 x^{2}) - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Multiply $3$ by $- 3$ .

$9 x^{4} - 9 x^{3} + 3 x^{2} \cdot 4 - x (3 x^{2}) - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Multiply $4$ by $3$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - x (3 x^{2}) - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Rewrite using the commutative property of multiplication.

$9 x^{4} - 9 x^{3} + 12 x^{2} - 1 \cdot 3 x \cdot x^{2} - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

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

Move $x^{2}$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - 1 \cdot 3 (x^{2} x) - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

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

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

$9 x^{4} - 9 x^{3} + 12 x^{2} - 1 \cdot 3 (x^{2} x^{1}) - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

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

$9 x^{4} - 9 x^{3} + 12 x^{2} - 1 \cdot 3 x^{2 + 1} - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Add $2$ and $1$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - 1 \cdot 3 x^{3} - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Multiply $- 1$ by $3$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - 3 x^{3} - x (- 3 x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Rewrite using the commutative property of multiplication.

$9 x^{4} - 9 x^{3} + 12 x^{2} - 3 x^{3} - 1 \cdot - 3 x \cdot x - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

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

Move $x$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - 3 x^{3} - 1 \cdot - 3 (x \cdot x) - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Multiply $x$ by $x$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - 3 x^{3} - 1 \cdot - 3 x^{2} - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Multiply $- 1$ by $- 3$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - 3 x^{3} + 3 x^{2} - x \cdot 4 - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Multiply $4$ by $- 1$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - 3 x^{3} + 3 x^{2} - 4 x - 5 (3 x^{2}) - 5 (- 3 x) - 5 \cdot 4$

Multiply $3$ by $- 5$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - 3 x^{3} + 3 x^{2} - 4 x - 15 x^{2} - 5 (- 3 x) - 5 \cdot 4$

Multiply $- 3$ by $- 5$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - 3 x^{3} + 3 x^{2} - 4 x - 15 x^{2} + 15 x - 5 \cdot 4$

Multiply $- 5$ by $4$ .

$9 x^{4} - 9 x^{3} + 12 x^{2} - 3 x^{3} + 3 x^{2} - 4 x - 15 x^{2} + 15 x - 20$

Simplify by adding terms.

Subtract $3 x^{3}$ from $- 9 x^{3}$ .

$9 x^{4} - 12 x^{3} + 12 x^{2} + 3 x^{2} - 4 x - 15 x^{2} + 15 x - 20$

Add $12 x^{2}$ and $3 x^{2}$ .

$9 x^{4} - 12 x^{3} + 15 x^{2} - 4 x - 15 x^{2} + 15 x - 20$

Combine the opposite terms in $9 x^{4} - 12 x^{3} + 15 x^{2} - 4 x - 15 x^{2} + 15 x - 20$ .

Subtract $15 x^{2}$ from $15 x^{2}$ .

$9 x^{4} - 12 x^{3} - 4 x + 0 + 15 x - 20$

Add $9 x^{4} - 12 x^{3} - 4 x$ and $0$ .

$9 x^{4} - 12 x^{3} - 4 x + 15 x - 20$

Add $- 4 x$ and $15 x$ .

$9 x^{4} - 12 x^{3} + 11 x - 20$

Write in Standard Form (3x^2-x-5)(3x^2-3x+4)

Related Questions

Support LCMGCF.com by disabling your adblocker.