Simplify (x^2-3y+1)(x^2+2x)

$(x^{2} - 3 y + 1) (x^{2} + 2 x)$

Step 1

Expand $(x^{2} - 3 y + 1) (x^{2} + 2 x)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x^{2} + x^{2} (2 x) - 3 y x^{2} - 3 y (2 x) + 1 x^{2} + 1 (2 x)$

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.

$x^{2 + 2} + x^{2} (2 x) - 3 y x^{2} - 3 y (2 x) + 1 x^{2} + 1 (2 x)$

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 3$ by $2$ .

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

Multiply $x^{2}$ by $1$ .

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

Multiply $2 x$ by $1$ .

$x^{4} + 2 x^{3} - 3 y x^{2} - 6 y x + x^{2} + 2 x$

Reorder.

Move $y$ .

$x^{4} + 2 x^{3} - 3 x^{2} y - 6 y x + x^{2} + 2 x$

Move $y$ .

$x^{4} + 2 x^{3} - 3 x^{2} y - 6 x y + x^{2} + 2 x$

Move $2 x^{3}$ .

$x^{4} - 3 x^{2} y + 2 x^{3} - 6 x y + x^{2} + 2 x$