Simplify (7x-5)^2

${(7 x - 5)}^{2}$

Step 1

Rewrite ${(7 x - 5)}^{2}$ as $(7 x - 5) (7 x - 5)$ .

$(7 x - 5) (7 x - 5)$

Step 2

Expand $(7 x - 5) (7 x - 5)$ using the FOIL Method.

Apply the distributive property.

$7 x (7 x - 5) - 5 (7 x - 5)$

Apply the distributive property.

$7 x (7 x) + 7 x \cdot - 5 - 5 (7 x - 5)$

Apply the distributive property.

$7 x (7 x) + 7 x \cdot - 5 - 5 (7 x) - 5 \cdot - 5$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot 7 x \cdot x + 7 x \cdot - 5 - 5 (7 x) - 5 \cdot - 5$

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

Move $x$ .

$7 \cdot 7 (x \cdot x) + 7 x \cdot - 5 - 5 (7 x) - 5 \cdot - 5$

Multiply $x$ by $x$ .

$7 \cdot 7 x^{2} + 7 x \cdot - 5 - 5 (7 x) - 5 \cdot - 5$

Multiply $7$ by $7$ .

$49 x^{2} + 7 x \cdot - 5 - 5 (7 x) - 5 \cdot - 5$

Multiply $- 5$ by $7$ .

$49 x^{2} - 35 x - 5 (7 x) - 5 \cdot - 5$

Multiply $7$ by $- 5$ .

$49 x^{2} - 35 x - 35 x - 5 \cdot - 5$

Multiply $- 5$ by $- 5$ .

$49 x^{2} - 35 x - 35 x + 25$

Subtract $35 x$ from $- 35 x$ .

$49 x^{2} - 70 x + 25$