BÀI TẬP8.13.Khai triển các đa thứca)$(x – 2)^{4}$;b)$(x +...

a) $(x - 2)^4 = [x + (-2)]^4 = C_4^0 \times x^4 + C_4^1 \times x^3 \times (-2) + C_4^2 \times x^2 \times (-2)^2 + C_4^3 \times x \times (-2)^3 + C_4^4 \times (-2)^4$$= 1 \times x^4 + 4 \times x^3 \times (-2) + 6 \times x^2 \times 4 + 4 \times x \times (-8) + 1 \times 16$$= x^4 - 8x^3 + 24x^2 - 32x + 16.$

b) $(x + 2)^5 = C_5^0 \times x^5 + C_5^1 \times x^4 \times 2 + C_5^2 \times x^3 \times 2^2 + C_5^3 \times x^2 \times 2^3 + C_5^4 \times x \times 2^4 + C_5^5 \times 2^5$$= 1 \times x^5 + 5 \times x^4 \times 2 + 10 \times x^3 \times 4 + 10 \times x^2 \times 8 + 5 \times x \times 16 + 1 \times 32$$= x^5 + 10x^4 + 40x^3 + 80x^2 + 80x + 32.$

c) $(2x + 3y)^4 = C_4^0 \times (2x)^4 + C_4^1 \times (2x)^3 \times 3y + C_4^2 \times (2x)^2 \times (3y)^2 + C_4^3 \times 2x \times (3y)^3 + C_4^4 \times (3y)$$= 1 \times 16x^4 + 4 \times 8x^3 \times 3y + 6 \times 4x^2 \times 9y^2 + 4 \times 2x \times 27y^3 + 1 \times 81y^4$$= 16x^4 + 96x^3y + 216x^2y^2 + 216xy^3 + 81y^4.$

d) $(2x - y)^5 = [2x + (-y)]^5 = C_5^0 \times (2x)^5 + C_5^1 \times (2x)^4 \times (-y) + C_5^2 \times (2x)^3 \times (-y)^2 + C_5^3 \times (2x)^2 \times (-y)^3$$= 1 \times 32x^5 + 5 \times 16x^4 \times (-y) + 10 \times 8x^3 \times y^2 + 10 \times 4x^2 \times (-y)^3 + 5 \times 2x \times y^4 + 1 \times (-y)^5$$= 32x^5 - 80x^4y + 80x^3y^2 - 40x^2y^3 + 10xy^4 - y^5.$