Question

Find the middle term in the expansion of (4x – 2y)2.​

Answer 1

Answer:

Students trying to do this expansion in their heads tend to mess up the powers. But this isn't the time to worry about that square on the x. I need to start my answer by plugging the terms and power into the Theorem. The first term in the binomial is "x2", the second term in "3", and the power n is 6, so, counting from 0 to 6, the Binomial Theorem gives me:

(x2 + 3)6 = 6C0 (x2)6(3)0 + 6C1 (x2)5(3)1 + 6C2 (x2)4(3)2 + 6C3 (x2)3(3)3

+ 6C4 (x2)2(3)4 + 6C5 (x2)1(3)5 + 6C6 (x2)0(3)6

Then simplifying gives me

(1)(x12)(1) + (6)(x10)(3) + (15)(x8)(9) + (20)(x6)(27)

+ (15)(x4)(81) + (6)(x2)(243) + (1)(1)(729)

= x12 + 18x10 + 135x8 + 540x6 + 1215x4 + 1458x2 + 729