Simplify (2a-5b)^2

${(2 a - 5 b)}^{2}$

Step 1

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

$(2 a - 5 b) (2 a - 5 b)$

Step 2

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

Apply the distributive property.

$2 a (2 a - 5 b) - 5 b (2 a - 5 b)$

Apply the distributive property.

$2 a (2 a) + 2 a (- 5 b) - 5 b (2 a - 5 b)$

Apply the distributive property.

$2 a (2 a) + 2 a (- 5 b) - 5 b (2 a) - 5 b (- 5 b)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a + 2 a (- 5 b) - 5 b (2 a) - 5 b (- 5 b)$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$2 \cdot 2 (a \cdot a) + 2 a (- 5 b) - 5 b (2 a) - 5 b (- 5 b)$

Multiply $a$ by $a$ .

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

Multiply $2$ by $2$ .

$4 a^{2} + 2 a (- 5 b) - 5 b (2 a) - 5 b (- 5 b)$

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 5$ .

$4 a^{2} - 10 a b - 5 b (2 a) - 5 b (- 5 b)$

Rewrite using the commutative property of multiplication.

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

Multiply $- 5$ by $2$ .

$4 a^{2} - 10 a b - 10 b a - 5 b (- 5 b)$

Rewrite using the commutative property of multiplication.

$4 a^{2} - 10 a b - 10 b a - 5 \cdot - 5 b \cdot b$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b$ .

$4 a^{2} - 10 a b - 10 b a - 5 \cdot - 5 b^{2}$

Multiply $- 5$ by $- 5$ .

$4 a^{2} - 10 a b - 10 b a + 25 b^{2}$

Subtract $10 b a$ from $- 10 a b$ .

Move $b$ .

$4 a^{2} - 10 a b - 10 a b + 25 b^{2}$

Subtract $10 a b$ from $- 10 a b$ .

$4 a^{2} - 20 a b + 25 b^{2}$

Simplify (2a-5b)^2

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