Answer
$${x^2}^2+(7x)^2+12^2+2x^2\cdot7x+2x^2\cdot12+2\cdot7x\cdot12=x^4+14x^3+73x^2+168x+144$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}{x^2}^2+(7x)^2+12^2+2x^2\cdot7x+2x^2\cdot12+2\cdot7x\cdot12& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}{x^2}^2+(7x)^2+12^2+2x^2\cdot7x+24x^2+2\cdot7x\cdot12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4+49x^2+144+2x^2\cdot7x+24x^2+2\cdot7x\cdot12 \xlongequal{ } \\[1 em] & \xlongequal{ }x^4+49x^2+144+14x^3+24x^2+14x\cdot12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^4+49x^2+144+14x^3+24x^2+168x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4+14x^3+73x^2+168x+144\end{aligned} $$ | |
| ① | $$ 2 x^2 \cdot 12 = 24 x^{2} $$ |
| ② | $$ \left( x^2 \right)^2 = 1^2 \left( x^2 \right)^2 = x^4 $$$$ \left( 7x \right)^2 = 7^2x^2 = 49x^2 $$$$ \left( 7x \right)^2 = 7^2x^2 = 49x^2 $$ |
| ③ | $$ 14 x \cdot 12 = 168 x $$ |
| ④ | Combine like terms: $$ x^4+ \color{blue}{49x^2} +144+14x^3+ \color{blue}{24x^2} +168x = x^4+14x^3+ \color{blue}{73x^2} +168x+144 $$ |
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