Question

Evaluate i) (a + b)³ + (a−b)³

Answer 1

Step-by-step explanation:

Expanding: (a+b)3−(a−b)3. =(a3+3a2b+3ab2+b3)−(a3−3a2b+3ab2−b3) . =6a2b+2b3. =2b(3a2+b2). If you are ...

Expanding: (a+b)3−(a−b)3 =(a3+3a2b+3ab2+b3)−(a3−3a2b+3ab2−b3) =6a2b+2b3 =2b(3a2+b2) If you are allowed

Answer 2

Given that , Deepak’s present age is one-third his mother’s present age and 6 years ago his mother’s age was five times of Deepak's age .

Exigency To Find : Present age of Deepak and his mother ??

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that , Present age of her mother be x yrs & Deepak's Present age be ⅓ × x yrs i.e., Deepak’s present age is one-third his mother’s present age .

$\begin{gathered}\\\qquad \bigstar \:\:\underline {\pmb{\sf {\purple { \:According \:To \:The \:Question \::\:}}}}\\\\\end{gathered}$

⠀⠀⠀━━⠀6 years ago his mother’s age was five times of Deepak's age .

$\begin{gathered} \\\qquad \dashrightarrow \sf \: \:\Big\{ \:Mothers's \:Age \:-\:6\:\Big\}\:=\:5\;\Big\{ \:Deepak's \:Age \:-\:6\:\Big\} \\\\\\\qquad \dashrightarrow \sf \: \:\Big\{ \:x \:-\:6\:\Big\}\:=\:5\;\bigg\{ \:\dfrac{1}{3}\:\times\:x \:-\:6\:\bigg\} \\\\\\ \qquad \dashrightarrow \sf \: \:\Big\{ \:x \:-\:6\:\Big\}\:=\:5\;\bigg\{ \:\dfrac{x}{3}\: \:-\:6\:\bigg\} \\\\\\ \qquad \dashrightarrow \sf \: \:\Big\{ \:x \:-\:6\:\Big\}\:=\:\;\bigg\{ \:\dfrac{5x}{3}\: \:-\:30\:\bigg\} \\\\\\ \qquad \dashrightarrow \sf \: \:\;\bigg\{ \:\dfrac{5x}{3}\: \:-\:x\:\bigg\} \:\:=\:-6\:+\:30\: \\\\\\ \qquad \dashrightarrow \sf \: \:\;\bigg\{ \:\dfrac{5x}{3}\: \:-\:x\:\bigg\} \:\:=\:24\: \\\\\\ \qquad \dashrightarrow \sf \: \:\;\bigg\{ \:\dfrac{5x\:-\:3x}{3}\: \:\bigg\} \:\:=\:24\: \\\\\ \qquad \dashrightarrow \sf \: \:\;\bigg\{ \:\dfrac{2x}{3}\: \:\bigg\} \:\:=\:24\: \\\\\\ \qquad \dashrightarrow \sf \: \:\;2x\: \: \:\:=\:24\:\times \:3\: \\\\\\ \qquad \dashrightarrow \sf \: \:\;2x\: \: \:\:=\:72\: \\\\\\ \qquad \dashrightarrow \sf \: \:\;x\: \: \:\:=\:\cancel{\dfrac{72}{2}}\: \\\\\\ \qquad \dashrightarrow \underline {\boxed {\pmb{\frak{ \: x\: \: \:\:=\:36\:yrs\;}}}}\:\:\bigstar \\\\\\\end{gathered}$

Therefore,

Mother’s present age is : x = 36 yrs &

Deepak’s present age is : ⅓ × x = ⅓ × 36 = 12 yrs .

$\qquad \therefore \:\underline {\sf \:Hence, \:Present \:ages \:of \:Deepak\:and \:his \:mother \:are \:\pmb{\bf 12 \:yrs\:} and \:\pmb{\bf 36 \:yrs \:}\:,respectively\:.}$