[tex] \red{ = > (2 {a}^{2} + 3b) {}^{2}} [/tex]
[tex] = ( {2 {a}^{2} )}^{2} + {(3b)}^{2} + 2(2 {a}^{2}) (3b)[/tex]
[tex] \orange{ = > \boxed{\blue{4 {a}^{4} + 9 {b}^{2} + 12 {a}^{2} b}}}[/tex]
[tex] \underline\color{teal}{(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy[/tex]
[tex] \red{ \mathbb{PLZ \: THANKs}}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow\pmb { \: \: (2a {}^{2} + 3b) {}^{2} } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow \: \underline{ \boxed{ \bf { \: (x + y) {}^{2} = x {}^{2} + 2xy + y {}^{2} \: } }}\\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow\pmb { \: \: (2a {}^{2} ) {}^{2} + 2 \times 2a {}^{2} \times 3b + (3b) {}^{2} } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow\pmb { \: \: 4a {}^{4} + 2 \times 2a {}^{2} \times 3b + (3b) {}^{2} } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow\pmb { \: \: 4a {}^{4} + 12a {}^{2} b + (3b) {}^{2} } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow \: \boxed{\sf \pink { \: \: 4a {}^{4} + 12a {}^{2}b + 9b {}^{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
Expand:-
[tex] \red{ = > (2 {a}^{2} + 3b) {}^{2}} [/tex]
[tex] = ( {2 {a}^{2} )}^{2} + {(3b)}^{2} + 2(2 {a}^{2}) (3b)[/tex]
[tex] \orange{ = > \boxed{\blue{4 {a}^{4} + 9 {b}^{2} + 12 {a}^{2} b}}}[/tex]
Identity used:-
[tex] \underline\color{teal}{(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy[/tex]
[tex] \red{ \mathbb{PLZ \: THANKs}}[/tex]
Gɪᴠᴇɴ :-
[tex] \begin{gathered}\\ \large\dashrightarrow\pmb { \: \: (2a {}^{2} + 3b) {}^{2} } \\ \end{gathered}[/tex]
Iᴅᴇɴᴛɪᴛʏ Usᴇᴅ :-
[tex] \begin{gathered}\\ \large\dashrightarrow \: \underline{ \boxed{ \bf { \: (x + y) {}^{2} = x {}^{2} + 2xy + y {}^{2} \: } }}\\ \end{gathered}[/tex]
Sᴏʟᴜᴛɪᴏɴ :-
[tex] \begin{gathered}\\ \large\dashrightarrow\pmb { \: \: (2a {}^{2} ) {}^{2} + 2 \times 2a {}^{2} \times 3b + (3b) {}^{2} } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow\pmb { \: \: 4a {}^{4} + 2 \times 2a {}^{2} \times 3b + (3b) {}^{2} } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow\pmb { \: \: 4a {}^{4} + 12a {}^{2} b + (3b) {}^{2} } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow \: \boxed{\sf \pink { \: \: 4a {}^{4} + 12a {}^{2}b + 9b {}^{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]