Expand (x+3)^6 using pascal's triangle

Question

slaaibak · Answer

Sixth row of the triangle: 1 6 15 20 15 6 1

so it's x^6 + 6 * x^5 * 3 + 15 * x^4 * 3^2 + 20 * x^3 * 3^3 + 15 * x^2 * 3^4 + 6 * x^1 * 3^ 5 + 3^6

slaaibak · Answer

Simplified: x^6+18 x^5+135 x^4+540 x^3+1215 x^2+1458 x+729

myininaya · Answer

1
n=1                         1             1
n=2                    1          2           1
n=3              1          3           3           1
n=4          1        4          6           4         1 
n=5       1      5        10         10         5       1
n=6    1     6       15        20        15       6        1
$$(x+y)^6=1 \cdot x^6y^0+6\cdot x^5y^1+15 \cdot x^4y^2+20\cdot x^3y^3+15\cdot x^2y^4+6 \cdot x^1y^5+1 \cdot x^0y^6$$

myininaya · Answer

replace y with 3

myininaya · Answer

that is y^6 at the end