Algebra Examples

${(a + b + c + d)}^{2}$

Step 1

Rewrite ${(a + b + c + d)}^{2}$ as $(a + b + c + d) (a + b + c + d)$ .

$(a + b + c + d) (a + b + c + d)$

Step 2

Expand $(a + b + c + d) (a + b + c + d)$ by multiplying each term in the first expression by each term in the second expression.

$a \cdot a + a b + a c + a d + b a + b \cdot b + b c + b d + c a + c b + c \cdot c + c d + d a + d b + d c + d \cdot d$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply $a$ by $a$ .

$a^{2} + a b + a c + a d + b a + b \cdot b + b c + b d + c a + c b + c \cdot c + c d + d a + d b + d c + d \cdot d$

Step 3.2

Multiply $b$ by $b$ .

$a^{2} + a b + a c + a d + b a + b^{2} + b c + b d + c a + c b + c \cdot c + c d + d a + d b + d c + d \cdot d$

Step 3.3

Multiply $c$ by $c$ .

$a^{2} + a b + a c + a d + b a + b^{2} + b c + b d + c a + c b + c^{2} + c d + d a + d b + d c + d \cdot d$

Step 3.4

Multiply $d$ by $d$ .

$a^{2} + a b + a c + a d + b a + b^{2} + b c + b d + c a + c b + c^{2} + c d + d a + d b + d c + d^{2}$

Step 4

Add $a b$ and $b a$ .

Tap for more steps...

Step 4.1

Reorder $b$ and $a$ .

$a^{2} + a b + a b + a c + a d + b^{2} + b c + b d + c a + c b + c^{2} + c d + d a + d b + d c + d^{2}$

Step 4.2

Add $a b$ and $a b$ .

$a^{2} + 2 a b + a c + a d + b^{2} + b c + b d + c a + c b + c^{2} + c d + d a + d b + d c + d^{2}$

Step 5

Add $a c$ and $c a$ .

Tap for more steps...

Step 5.1

Reorder $c$ and $a$ .

$a^{2} + 2 a b + a d + b^{2} + b c + b d + a c + a c + c b + c^{2} + c d + d a + d b + d c + d^{2}$

Step 5.2

Add $a c$ and $a c$ .

$a^{2} + 2 a b + a d + b^{2} + b c + b d + 2 a c + c b + c^{2} + c d + d a + d b + d c + d^{2}$

Step 6

Add $a d$ and $d a$ .

Tap for more steps...

Step 6.1

Reorder $d$ and $a$ .

$a^{2} + 2 a b + b^{2} + b c + b d + 2 a c + c b + c^{2} + c d + a d + a d + d b + d c + d^{2}$

Step 6.2

Add $a d$ and $a d$ .

$a^{2} + 2 a b + b^{2} + b c + b d + 2 a c + c b + c^{2} + c d + 2 a d + d b + d c + d^{2}$

Step 7

Add $b c$ and $c b$ .

Tap for more steps...

Step 7.1

Reorder $c$ and $b$ .

$a^{2} + 2 a b + b^{2} + b c + b c + b d + 2 a c + c^{2} + c d + 2 a d + d b + d c + d^{2}$

Step 7.2

Add $b c$ and $b c$ .

$a^{2} + 2 a b + b^{2} + 2 b c + b d + 2 a c + c^{2} + c d + 2 a d + d b + d c + d^{2}$

Step 8

Add $b d$ and $d b$ .

Tap for more steps...

Step 8.1

Reorder $d$ and $b$ .

$a^{2} + 2 a b + b^{2} + 2 b c + 2 a c + c^{2} + c d + 2 a d + b d + b d + d c + d^{2}$

Step 8.2

Add $b d$ and $b d$ .

$a^{2} + 2 a b + b^{2} + 2 b c + 2 a c + c^{2} + c d + 2 a d + 2 b d + d c + d^{2}$

Step 9

Add $c d$ and $d c$ .

Tap for more steps...

Step 9.1

Reorder $d$ and $c$ .

$a^{2} + 2 a b + b^{2} + 2 b c + 2 a c + c^{2} + c d + c d + 2 a d + 2 b d + d^{2}$

Step 9.2

Add $c d$ and $c d$ .

$a^{2} + 2 a b + b^{2} + 2 b c + 2 a c + c^{2} + 2 c d + 2 a d + 2 b d + d^{2}$

Step 10

Move $2 c d$ .

$a^{2} + 2 a b + b^{2} + 2 b c + 2 a c + c^{2} + 2 a d + 2 b d + 2 c d + d^{2}$

Step 11

Move $c^{2}$ .

$a^{2} + 2 a b + b^{2} + 2 b c + 2 a c + 2 a d + 2 b d + c^{2} + 2 c d + d^{2}$

Step 12

Move $2 b c$ .

$a^{2} + 2 a b + b^{2} + 2 a c + 2 a d + 2 b c + 2 b d + c^{2} + 2 c d + d^{2}$

Step 13

Move $b^{2}$ .

$a^{2} + 2 a b + 2 a c + 2 a d + b^{2} + 2 b c + 2 b d + c^{2} + 2 c d + d^{2}$