Expand the Trigonometric Expression (2x-5)^2

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

Step 1

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

$(2 x - 5) (2 x - 5)$

Step 2

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

Apply the distributive property.

$2 x (2 x - 5) - 5 (2 x - 5)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 5$ by $2$ .

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

Multiply $2$ by $- 5$ .

$4 x^{2} - 10 x - 10 x - 5 \cdot - 5$

Multiply $- 5$ by $- 5$ .

$4 x^{2} - 10 x - 10 x + 25$

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

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