The binomial expansion of (2x+y)^12 can be represented by the binomial theorem as follows:

(2x+y)^12 = Σ (from k=0 to 12) [12Ck * (2x)^(12-k) * (y)^k]

The term ax^5y^7 corresponds to the case where k=7 (because the power of y is 7). So, we substitute k=7 into the binomial theorem:

a = 12C7 * (2x)^(12-7) * (y)^7
a = 792 * (2x)^5 * y^7
a = 792 * 32x^5 * y^7
a = 25344x^5 * y^7

So, the coefficient a for the term ax^5y^7 of the binomial expansion of (2x+y)^12 is 25344.

Question

The binomial expansion of (2x+y)^12 can be represented by the binomial theorem as follows:

(2x+y)^12 = Σ (from k=0 to 12) [12Ck * (2x)^(12-k) * (y)^k]

The term ax^5y^7 corresponds to the case where k=7 (because the power of y is 7). So, we substitute k=7 into the binomial theorem:

a = 12C7 * (2x)^(12-7) * (y)^7
a = 792 * (2x)^5 * y^7
a = 792 * 32x^5 * y^7
a = 25344x^5 * y^7

So, the coefficient a for the term ax^5y^7 of the binomial expansion of (2x+y)^12 is 25344.

Knowee AI · Accepted Answer

The binomial expansion of (2x+y)^12 can be represented by the binomial theorem as follows:

(2x+y)^12 = Σ (from k=0 to 12) [12Ck * (2x)^(12-k) * (y)^k]

The term ax^5y^7 corresponds to the case where k=7 (because the power of y is 7). So, we substitute k=7 into the binomial theorem:

a = 12C7 * (2x)^(12-7) * (y)^7
a = 792 * (2x)^5 * y^7
a = 792 * 32x^5 * y^7
a = 25344x^5 * y^7

So, the coefficient a for the term ax^5y^7 of the binomial expansion of (2x+y)^12 is 25344.

Determine the coefficient, a, for the term ax5y7 of the binomial expansion of (2x+y)12.