Algebra Examples

${(2 x + y)}^{6}$

Step 1

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

Tap for more steps...

Step 1.1

Use the Binomial Theorem.

${(2 x)}^{6} + 6 {(2 x)}^{5} y + 15 {(2 x)}^{4} y^{2} + 20 {(2 x)}^{3} y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Apply the product rule to $2 x$ .

$2^{6} x^{6} + 6 {(2 x)}^{5} y + 15 {(2 x)}^{4} y^{2} + 20 {(2 x)}^{3} y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.2

Raise $2$ to the power of $6$ .

$64 x^{6} + 6 {(2 x)}^{5} y + 15 {(2 x)}^{4} y^{2} + 20 {(2 x)}^{3} y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.3

Apply the product rule to $2 x$ .

$64 x^{6} + 6 (2^{5} x^{5}) y + 15 {(2 x)}^{4} y^{2} + 20 {(2 x)}^{3} y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.4

Raise $2$ to the power of $5$ .

$64 x^{6} + 6 (32 x^{5}) y + 15 {(2 x)}^{4} y^{2} + 20 {(2 x)}^{3} y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.5

Multiply $32$ by $6$ .

$64 x^{6} + 192 x^{5} y + 15 {(2 x)}^{4} y^{2} + 20 {(2 x)}^{3} y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.6

Apply the product rule to $2 x$ .

$64 x^{6} + 192 x^{5} y + 15 (2^{4} x^{4}) y^{2} + 20 {(2 x)}^{3} y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.7

Raise $2$ to the power of $4$ .

$64 x^{6} + 192 x^{5} y + 15 (16 x^{4}) y^{2} + 20 {(2 x)}^{3} y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.8

Multiply $16$ by $15$ .

$64 x^{6} + 192 x^{5} y + 240 x^{4} y^{2} + 20 {(2 x)}^{3} y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.9

Apply the product rule to $2 x$ .

$64 x^{6} + 192 x^{5} y + 240 x^{4} y^{2} + 20 (2^{3} x^{3}) y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.10

Raise $2$ to the power of $3$ .

$64 x^{6} + 192 x^{5} y + 240 x^{4} y^{2} + 20 (8 x^{3}) y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.11

Multiply $8$ by $20$ .

$64 x^{6} + 192 x^{5} y + 240 x^{4} y^{2} + 160 x^{3} y^{3} + 15 {(2 x)}^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.12

Apply the product rule to $2 x$ .

$64 x^{6} + 192 x^{5} y + 240 x^{4} y^{2} + 160 x^{3} y^{3} + 15 (2^{2} x^{2}) y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.13

Raise $2$ to the power of $2$ .

$64 x^{6} + 192 x^{5} y + 240 x^{4} y^{2} + 160 x^{3} y^{3} + 15 (4 x^{2}) y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.14

Multiply $4$ by $15$ .

$64 x^{6} + 192 x^{5} y + 240 x^{4} y^{2} + 160 x^{3} y^{3} + 60 x^{2} y^{4} + 6 (2 x) y^{5} + y^{6}$

Step 1.2.15

Multiply $2$ by $6$ .

$64 x^{6} + 192 x^{5} y + 240 x^{4} y^{2} + 160 x^{3} y^{3} + 60 x^{2} y^{4} + 12 x y^{5} + y^{6}$

Step 2

The leading term in a polynomial is the term with the highest degree.

$64 x^{6}$

Step 3

The leading coefficient in a polynomial is the coefficient of the leading term.

$64$