How do you expand $(2x + y)^4$ using Pascal’s Triangle?

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Answer 1 · 2015-07-19T12:50:14

Combine the $5$ th row of Pascal's triangle and a sequence of powers of $2$ to find the coefficients of the expansion:

$(2x+y)^4 = 16x^4+32x^3y+24x^2y^2+8xy^3+y^4$

Write out the $5$ th row of Pascal's triangle as a sequence:

$1, 4, 6, 4, 1$

Write out descending powers of $2$ from $2^4$ to $2^0$ as a sequence:

$16, 8, 4, 2, 1$

Multiply the two sequences together to get:

$16, 32, 24, 8, 1$

These are the coefficients of the expansion:

$(2x+y)^4 = 16x^4+32x^3y+24x^2y^2+8xy^3+y^4$

How do you expand (2x + y)^4 (2x + y)^4 using Pascal’s Triangle?