Homework SourseUse the Binomial Theorem to expand the binomial and express
Use the Binomial Theorem to expand the binomial and express the result in simplified form. (2x-y)^5 (2x-y)^5= 
Solution
Binomial theorem ==> (a + b)n = nc0 anb0 + nc1 an-1b1 + nc2 an-2b2 + --- + ncr an-rbr + ---- + ncn a0bn
==> (2x -y)5 = 5c0 (2x)5(-y)0 + 5c1 (2x)5-1(-y)1 + 5c2 (2x)5-2(-y)2 + 5c3 (2x)5-3(-y)3 + 5c4 (2x)5-4(-y)4 + 5c5 (2x)5-5(-y)5
==> (2x -y)5 = 32x5 + 5(16x4)(-y) + 10 (8x3)(y)2 +10 (4x2)(-y)3 + 5 (2x)(-y)4 + 1 (-y)5
==> (2x -y)5 = 32x5 - 80x4y + 80x3y2 -40x2y3 + 10xy4 - y5
