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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

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

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

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

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $- 1$ .

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

Multiply $4$ by $3$ .

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

Simplify by adding terms.

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

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

Subtract $3 x^{2}$ from $4 x^{2}$ .

$x^{4} + 2 x^{3} + x^{2} + 12 x$

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

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