Question

Simplify: $x^5+10x^{4}a+40x^3{a}^2+80x^2{a}^3+80x{a}^4+32a^5$

Answer 1

Binomial Expansion for positive Integral

Index -

Simplify: $x^5+10x^{4}a+40x^3{a}^2+80x^2{a}^3+80x{a}^4+32a^5$

binomial expansion of $(x+a{)}^n{=}^n{C}_0{x}^n{+}^n{C}_1{x}^{n-1}a+...$

$....{+}^n{C}_r{x}^{n-r}{a}^r+...$

${+}^n{C}_n{x}^{.}{a}^n$

Now,

$(x+2a{)}^5={}^5{C}_0{x}^5{+}^5{C}_1{x}^4(2a\left){+}^5{C}_2{x}^3\right(2a{)}^2+$

${}^5{C}_3{x}^2\left(2a{)}^3{+}^5{C}_4\right(2a{)}^{4}x{+}^5{C}_5(2a{)}^5$

$(x+2a{)}^5=x^5+10a{x}^4+10\times 4a^2{x}^3+10\times 8a^3{x}^2$

$+5\times 16a^{4}x+32a^5$

$(x+2a{)}^5=x^5+10x^{4}a+40x^3{a}^2+80x^2{a}^3+80x{a}^4$

$+32a^5$