Question

Question 1 Expand the expression (1– 2x)^5

Class X1 - Maths -Binomial Theorem Page 166

Answer 1

(1-2x)⁵
use the formula,
(x-y)ⁿ = ⁿC₀xⁿ -ⁿC₁xⁿ⁻¹.y +ⁿC₂xⁿ⁻².y².......(-1)ⁿ.ⁿCₙyⁿ.

Now,
(1 - 2x)^5 = 5C0.(1)^5 - 5C1.(1)^4.2x + 5C2(1)³.(2x)² - 5C3(1)².(2x)³ + 5C4.(1)¹.(2x)⁴ - 5C5(2x)^5

= 5C0 - 5C1(2x) + 5C2(4x²) - 5C3(8x³) + 5C4(16x⁴) - 5C5(32x^5)

= 5!/0!×5! - 5×4!/1!×4!(2x) + 5×4×3!/2!×3!(4x²) - 5×4×3!/3!×2! + 5×4!/4!×1!(16x⁴)-5!/0!×5!(32x^5)

= 1 - 10x + 40x² - 80x³ + 80x⁴ -32x^5

Answer 2

I HOPE IT WILL HELP YOU.

THANK YOU.