Answer:
Here is written in the bracket
[2\5x +5/6y]
Then,we need to open both the bracket and to take the LCM
LCM of 5and 6=30
2/5= we will multiply it with 6
it will be 2*6/5*6 = 12/30
5*5/6*5= 25/30
Then we will make it as a equivalent fractions
12/30 + 25/30 = 12+25/30
= 37/30xy
hopes it helpful
[tex] \begin{gathered}\\ \large\dashrightarrow\sf { \: \: \bigg( \frac{2}{5} x + \frac{5}{6} y \bigg) {}^{2} } \\ \end{gathered}[/tex]
[tex]\begin{gathered}\\ \large\dashrightarrow \: \underline{ \boxed{\bf { \: \: \bigg( x + y \bigg) {}^{2} = x {}^{2} + 2xy + y {}^{2} }} } \\ \end{gathered}[/tex]
[tex]\begin{gathered}\\ \large\dashrightarrow\sf { \: \: \bigg( \frac{2}{5} x \bigg) {}^{2} + 2 \times \frac{2}{5} x \times \frac{5}{6} y + \bigg( \frac{5}{6} y\bigg) {}^{2} } \\ \end{gathered}[/tex]
[tex]\begin{gathered}\\ \large\dashrightarrow\sf { \: \frac{4}{25}x {}^{2} + 2 \times \frac{2}{5} x \times \frac{5}{6} y + \bigg( \frac{5}{6}y \bigg) {}^{2} \: } \\ \end{gathered}[/tex]
[tex]\begin{gathered}\\ \large\dashrightarrow\sf { \: \frac{4}{25} \times x {}^{2} + \frac{2}{3} xy + \bigg( \frac{5}{6} y \bigg) {}^{2} \: } \\ \end{gathered}[/tex]
[tex]\begin{gathered}\\ \large\dashrightarrow \: \boxed{\sf \red { \: \frac{4}{25} x {}^{2} + \frac{2}{3}xy + \frac{25}{36 {}^{} } y {}^{2} \: } } \\ \end{gathered}[/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \small \color{blue}{ \underline{\boxed{ \begin{array}{cc} \small \underline{\underline{\bf{ \color{red}{{ \orange \bigstar \: MᴏʀE \: IᴅᴇɴᴛɪᴛɪᴇS \: \orange \bigstar}}}}} \\ \\ \: \frak{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \: \frak{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \: \frak{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \: \frak{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \: \frak{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \: \frak{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \: \frak{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \: \frak{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \\ \: \end{array} }}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \: \: [/tex]
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Verified answer
Answer:
Here is written in the bracket
[2\5x +5/6y]
Then,we need to open both the bracket and to take the LCM
LCM of 5and 6=30
2/5= we will multiply it with 6
it will be 2*6/5*6 = 12/30
5*5/6*5= 25/30
Then we will make it as a equivalent fractions
12/30 + 25/30 = 12+25/30
= 37/30xy
hopes it helpful
Gɪᴠᴇɴ :-
[tex] \begin{gathered}\\ \large\dashrightarrow\sf { \: \: \bigg( \frac{2}{5} x + \frac{5}{6} y \bigg) {}^{2} } \\ \end{gathered}[/tex]
Iᴅᴇɴᴛɪᴛʏ Usᴇᴅ :-
[tex]\begin{gathered}\\ \large\dashrightarrow \: \underline{ \boxed{\bf { \: \: \bigg( x + y \bigg) {}^{2} = x {}^{2} + 2xy + y {}^{2} }} } \\ \end{gathered}[/tex]
Sᴏʟᴜᴛɪᴏɴ :-
[tex]\begin{gathered}\\ \large\dashrightarrow\sf { \: \: \bigg( \frac{2}{5} x \bigg) {}^{2} + 2 \times \frac{2}{5} x \times \frac{5}{6} y + \bigg( \frac{5}{6} y\bigg) {}^{2} } \\ \end{gathered}[/tex]
[tex]\begin{gathered}\\ \large\dashrightarrow\sf { \: \frac{4}{25}x {}^{2} + 2 \times \frac{2}{5} x \times \frac{5}{6} y + \bigg( \frac{5}{6}y \bigg) {}^{2} \: } \\ \end{gathered}[/tex]
[tex]\begin{gathered}\\ \large\dashrightarrow\sf { \: \frac{4}{25} \times x {}^{2} + \frac{2}{3} xy + \bigg( \frac{5}{6} y \bigg) {}^{2} \: } \\ \end{gathered}[/tex]
[tex]\begin{gathered}\\ \large\dashrightarrow \: \boxed{\sf \red { \: \frac{4}{25} x {}^{2} + \frac{2}{3}xy + \frac{25}{36 {}^{} } y {}^{2} \: } } \\ \end{gathered}[/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Additional information :-
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \small \color{blue}{ \underline{\boxed{ \begin{array}{cc} \small \underline{\underline{\bf{ \color{red}{{ \orange \bigstar \: MᴏʀE \: IᴅᴇɴᴛɪᴛɪᴇS \: \orange \bigstar}}}}} \\ \\ \: \frak{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \: \frak{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \: \frak{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \: \frak{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \: \frak{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \: \frak{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \: \frak{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \: \frak{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \\ \: \end{array} }}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \: \: [/tex]