+23252 Beside the obvious way of multiplying this, factor by factor, you can use this expansion:
(a + b)5 = 5C0 · a5 · b0 + 5C1 · a4 · b1 + 5C2 · a3 · b2 + 5C3 · a2 · b3 + 5C4 · a1 · b4 + 5C5 · a0 · b5
In this problem: a = 2x b = -1:
(2x - 1)5 = 5C0(2x)5(-1)0 + 5C1(2x)4(-1)1 + 5C2(2x)3(-1)2 + 5C3(2x)2(-1)3 + 5C4(2x)1(-1)4 + 5C5(2x)0(-1)5
= (1)(32x5)(1) + (5)(16x4)(-1) + (10)(8x3)(1) + (10)(4x2)(-1) + (5)(2x)(1) + (1)(1)(-1)
= 32x5 - 80x4 + 80x3 - 40x + 10x - 1
+23252 Beside the obvious way of multiplying this, factor by factor, you can use this expansion:
(a + b)5 = 5C0 · a5 · b0 + 5C1 · a4 · b1 + 5C2 · a3 · b2 + 5C3 · a2 · b3 + 5C4 · a1 · b4 + 5C5 · a0 · b5
In this problem: a = 2x b = -1:
(2x - 1)5 = 5C0(2x)5(-1)0 + 5C1(2x)4(-1)1 + 5C2(2x)3(-1)2 + 5C3(2x)2(-1)3 + 5C4(2x)1(-1)4 + 5C5(2x)0(-1)5
= (1)(32x5)(1) + (5)(16x4)(-1) + (10)(8x3)(1) + (10)(4x2)(-1) + (5)(2x)(1) + (1)(1)(-1)
= 32x5 - 80x4 + 80x3 - 40x + 10x - 1
