Question

(1 - √2y)^3 solve using identities class 9

Answer 1

$\large\bf\underline\red{Answer \: :-}$

Given : (1 - √2y)³

Here,

We use the formula (a - b)³ = =a³ - 3ab(a - b) - b³

By using formula

$\sf\longmapsto{(1) {}^{3} - 3(1)( \sqrt{2} y)(1 - \sqrt{2}y) - ( \sqrt{2} y) {}^{3} } \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\longmapsto{1 - 3 \sqrt{2} y (1 - \sqrt{2} y) - ( \sqrt{2} y \times \sqrt{2}y \times \sqrt{2} y) } \\ \\ \sf\longmapsto{1 - 3 \sqrt{2}y - 3(2)y -( 2y {}^{2} \times \sqrt{2} y) } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\\ \\ \bf\longmapsto \red{1 - 3 \sqrt{2}y - 6y - 2 \sqrt{2} y {}^{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Important identities :

$\begin{gathered}\boxed{\begin{array}{c} \\ \tiny\bf{\dag}\:\underline{\frak{\rm{S}\frak{ome\:important\:algebric\:identities\:::}}} \\\\ \green{\bigstar}\:\rm \red{ (A+B)^{2} = A^{2} + 2AB + B^{2}} \\\\ \red{\bigstar}\rm\: \green{(A-B)^{2} = A^{2} - 2AB + B^{2}} \\\\ \orange{\bigstar}\rm\: \blue{A^{2} - B^{2} = (A+B)(A-B)}\\\\ \blue{\bigstar}\rm\: \orange{(A+B)^{2} = (A-B)^{2} + 4AB}\\\\ \purple{\bigstar}\rm\: \purple{(A-B)^{2} = (A+B)^{2} - 4AB}\\\\ \purple{\bigstar} \rm\: \pink{(A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}}\\\\ \blue{\bigstar}\rm\:(A-B)^{3} = A^{3} - 3AB(A-B) - B^{3}\\\\ \bigstar\rm\: \pink{A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})} \\\\ \end{array}}\end{gathered}$