Question

Expand the following binomials: ${(x-3)}^5$

• A. $x^5+25x^4+90x^3-270x^2+405x-243$
• B. $x^5-15x^4+90x^3-270x^2-405x-243$
• C. $x^5-15x^4+80x^3-270x^2+405x-243$
• D. $x^5-15x^4+90x^3-270x^2+405x-243$

Answer 1

The correct option is D $x^5-15x^4+90x^3-270x^2+405x-243$

${(x-3)}^5{=}^5{\text{C}}_0{x}^5{+}^5{\text{C}}_1{x}^4{(-3)}^1{+}^5{\text{C}}_2{x}^3{(-3)}^2{+}^5{\text{C}}_3{x}^2{(-3)}^3{+}^5{\text{C}}_{4}x{(-3)}^4{+}^5{\text{C}}_5{(-3)}^5$
$=x^5-15x^4+90x^3-270x^2+405x-243$