Simplify x^2+x(x-5)^2

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

Step 1

Simplify each term.

Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

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

Expand $(x - 5) (x - 5)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 5$ to the left of $x$ .

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

Multiply $- 5$ by $- 5$ .

$x^{2} + x (x^{2} - 5 x - 5 x + 25)$

Subtract $5 x$ from $- 5 x$ .

$x^{2} + x (x^{2} - 10 x + 25)$

Apply the distributive property.

$x^{2} + x \cdot x^{2} + x (- 10 x) + x \cdot 25$

Simplify.

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

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

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

$x^{2} + x^{1} x^{2} + x (- 10 x) + x \cdot 25$

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

$x^{2} + x^{1 + 2} + x (- 10 x) + x \cdot 25$

Add $1$ and $2$ .

$x^{2} + x^{3} + x (- 10 x) + x \cdot 25$

Rewrite using the commutative property of multiplication.

$x^{2} + x^{3} - 10 x \cdot x + x \cdot 25$

Move $25$ to the left of $x$ .

$x^{2} + x^{3} - 10 x \cdot x + 25 \cdot x$

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

Move $x$ .

$x^{2} + x^{3} - 10 (x \cdot x) + 25 \cdot x$

Multiply $x$ by $x$ .

$x^{2} + x^{3} - 10 x^{2} + 25 \cdot x$

$x^{2} + x^{3} - 10 x^{2} + 25 x$

Step 2

Subtract $10 x^{2}$ from $x^{2}$ .

$x^{3} - 9 x^{2} + 25 x$

Simplify x^2+x(x-5)^2

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