Question

The middle terms in the expansion of $(x^2-a^2{)}^5$ is

• A. $10x^6{a}^4,-10x^4{a}^6$
• B. $-10x^6{a}^4,10x^4{a}^6$
• C. $10x^6{a}^4,10x^4{a}^6$
• D. $-10x^6{a}^4,-10x^4{a}^6$

Answer 1

The correct option is A $10x^6{a}^4,-10x^4{a}^6$

$(a\pm b{)}^n{=}^n{C}_0{a}^n{b}^0{\pm }^n{C}_1{a}^{n-1}{b}^1{+}^n{C}_2{a}^{n-2}{b}^2\pm ....{+}^n{C}_n{a}^0{b}^n$

$(x^2-a^2{)}^5{=}^5{C}_0{x}^{10}{-}^5{C}_1{x}^8{a}^2{+}^5{C}_2{x}^6{a}^4{-}^5{C}_3{x}^4{a}^6{+}^5{C}_4{x}^2{a}^8{-}^5{C}_5{x}^0{a}^{10}$

$=x^{10}-5x^8{a}^2+10x^6{a}^4-10x^4{a}^6+5x^2{a}^8-x^0{a}^{10}$

Middle term = $10x^6{a}^4,-10x^4{a}^6$