Solution 44 Page 18 Math Workbook 10 – Kite>


Topic

Expand the following expressions:

a) \({(x – 2y)^4}\) b) \({( – 3x – y)^5}\)

Solution method – See details

a) Apply the expansion formula: \({(a – b)^4} = {a^4} – 4{a^3}b + 6{a^2}{b^2} – 4a{b ^3} + {b^4}\) with \(a = x,b = 2y\)

b) Apply the expansion formula: \({(a – b)^5} = {a^5} – 5{a^4}b + 10{a^3}{b^2} – 10{a ^2}{b^3} + 5a{b^4} – {b^5}\) with \(a = – 3x,b = y\)

Detailed explanation

a) \({(x – 2y)^4} = {x^4} – 4{x^3}.2y + 6{x^2}. {(2y)^2} – 4x. {(2y) ^3} + {(2y)^4}\)\( = {x^4} – 8{x^3}y + 24{x^2}{y^2} – 32x{y^3} + 16 {y^4}\)

b) \({( – 3x – y)^5} = {( – 3x)^5} – 5. {( – 3x)^4}y + 10. {( – 3x)^3}. {y^ 2} – 10. {( – 3x)^2}. {y^3} + 5.( – 3x) {y^4} – {y^5}\)

\( = – 243{x^5} – 405{x^4}y – 270{x^3}{y^2} – 90{x^2}{y^3} – 15x{y^4} – {y^5}\)



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