Simplify (2x-5)^2-(x+3)(x-3)

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

Step 1

Simplify each term.

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

$(2 x - 5) (2 x - 5) - (x + 3) (x - 3)$

Expand $(2 x - 5) (2 x - 5)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x - 5) - 5 (2 x - 5) - (x + 3) (x - 3)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 5 - 5 (2 x - 5) - (x + 3) (x - 3)$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5 - (x + 3) (x - 3)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5 - (x + 3) (x - 3)$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot - 5 - 5 (2 x) - 5 \cdot - 5 - (x + 3) (x - 3)$

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 5$ by $2$ .

$4 x^{2} - 10 x - 5 (2 x) - 5 \cdot - 5 - (x + 3) (x - 3)$

Multiply $2$ by $- 5$ .

$4 x^{2} - 10 x - 10 x - 5 \cdot - 5 - (x + 3) (x - 3)$

Multiply $- 5$ by $- 5$ .

$4 x^{2} - 10 x - 10 x + 25 - (x + 3) (x - 3)$

Subtract $10 x$ from $- 10 x$ .

$4 x^{2} - 20 x + 25 - (x + 3) (x - 3)$

Apply the distributive property.

$4 x^{2} - 20 x + 25 + (- x - 1 \cdot 3) (x - 3)$

Multiply $- 1$ by $3$ .

$4 x^{2} - 20 x + 25 + (- x - 3) (x - 3)$

Expand $(- x - 3) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$4 x^{2} - 20 x + 25 - x (x - 3) - 3 (x - 3)$

Apply the distributive property.

$4 x^{2} - 20 x + 25 - x \cdot x - x \cdot - 3 - 3 (x - 3)$

Apply the distributive property.

$4 x^{2} - 20 x + 25 - x \cdot x - x \cdot - 3 - 3 x - 3 \cdot - 3$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$4 x^{2} - 20 x + 25 - (x \cdot x) - x \cdot - 3 - 3 x - 3 \cdot - 3$

Multiply $x$ by $x$ .

$4 x^{2} - 20 x + 25 - x^{2} - x \cdot - 3 - 3 x - 3 \cdot - 3$

Multiply $- 3$ by $- 1$ .

$4 x^{2} - 20 x + 25 - x^{2} + 3 x - 3 x - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$4 x^{2} - 20 x + 25 - x^{2} + 3 x - 3 x + 9$

Subtract $3 x$ from $3 x$ .

$4 x^{2} - 20 x + 25 - x^{2} + 0 + 9$

Add $- x^{2}$ and $0$ .

$4 x^{2} - 20 x + 25 - x^{2} + 9$

Step 2

Simplify by adding terms.

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

$3 x^{2} - 20 x + 25 + 9$

Add $25$ and $9$ .

$3 x^{2} - 20 x + 34$

Simplify (2x-5)^2-(x+3)(x-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.