Algebra Examples

${(a + 2 b - 10)}^{2}$

Step 1

Rewrite ${(a + 2 b - 10)}^{2}$ as $(a + 2 b - 10) (a + 2 b - 10)$ .

$(a + 2 b - 10) (a + 2 b - 10)$

Step 2

Expand $(a + 2 b - 10) (a + 2 b - 10)$ by multiplying each term in the first expression by each term in the second expression.

$a \cdot a + a (2 b) + a \cdot - 10 + 2 b a + 2 b (2 b) + 2 b \cdot - 10 - 10 a - 10 (2 b) - 10 \cdot - 10$

Step 3

Simplify each term.

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Step 3.1

Multiply $a$ by $a$ .

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

Step 3.2

Rewrite using the commutative property of multiplication.

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

Step 3.3

Move $- 10$ to the left of $a$ .

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

Step 3.4

Rewrite using the commutative property of multiplication.

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

Step 3.5

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

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Step 3.5.1

Move $b$ .

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

Step 3.5.2

Multiply $b$ by $b$ .

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

Step 3.6

Multiply $2$ by $2$ .

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

Step 3.7

Multiply $- 10$ by $2$ .

$a^{2} + 2 a b - 10 a + 2 b a + 4 b^{2} - 20 b - 10 a - 10 (2 b) - 10 \cdot - 10$

Step 3.8

Multiply $2$ by $- 10$ .

$a^{2} + 2 a b - 10 a + 2 b a + 4 b^{2} - 20 b - 10 a - 20 b - 10 \cdot - 10$

Step 3.9

Multiply $- 10$ by $- 10$ .

$a^{2} + 2 a b - 10 a + 2 b a + 4 b^{2} - 20 b - 10 a - 20 b + 100$

Step 4

Add $2 a b$ and $2 b a$ .

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Step 4.1

Move $b$ .

$a^{2} - 10 a + 2 a b + 2 a b + 4 b^{2} - 20 b - 10 a - 20 b + 100$

Step 4.2

Add $2 a b$ and $2 a b$ .

$a^{2} - 10 a + 4 a b + 4 b^{2} - 20 b - 10 a - 20 b + 100$

Step 5

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

$a^{2} - 20 a + 4 a b + 4 b^{2} - 20 b - 20 b + 100$

Step 6

Subtract $20 b$ from $- 20 b$ .

$a^{2} - 20 a + 4 a b + 4 b^{2} - 40 b + 100$

Step 7

Move $- 20 a$ .

$a^{2} + 4 a b + 4 b^{2} - 20 a - 40 b + 100$