[size=150]Select [b]all[/b] the expressions that are perfect squares.[/size]

How are the contents of the three diagrams alike?

[size=150]This diagram represents [math](\text{term_1 + term_2})^2[/math]. [/size][br][center][img]data:image/png;base64,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[/img][/center][br]Describe your observations about cells 1, 2, 3, and 4.

Rewrite the perfect-square expression [math]\left(n+7\right)^2[/math] in standard form: [math]ax^2+bx+c[/math].[br]

Rewrite the perfect-square expression [math]\left(5-m\right)^2[/math] in standard form: [math]ax^2+bx+c[/math].[br]

Rewrite the perfect-square expression [math]\left(h+\frac{1}{3}\right)^2[/math] in standard form: [math]ax^2+bx+c[/math].[br]

How are the [math]ax^2[/math], [math]bx[/math], and [math]c[/math] of a perfect square in standard form related to the two terms in [math](\text{term_1 + term_2})^2[/math]?[br]

[math]\left(x-1\right)^2=4[/math]

[math]\left(x+5\right)^2=89[/math]

[math]\left(x-2\right)^2=0[/math]

[math]\left(x+11\right)^2=121[/math]

[math]\left(x-7\right)^2=\frac{64}{49}[/math]

[size=150]Explain or show why the product of a sum and a difference, such as [math]\left(2x+1\right)\left(2x-1\right)[/math], has no linear term when written in standard form.[/size]

[size=150]To solve the equation [math](x+3)^2=4[/math], Han first expanded the squared expression.[br][br]Here is his incomplete work:[/size][br][math]\begin{align}(x+3)^2&=4\\ (x+3)(x+3)&=4\\ x^2+3x+3x+9&=4\\ x^2+6x+9&=4 \end{align}[/math][br][br]Complete Han’s work and solve the equation.

[size=150]Jada saw the equation [math]\left(x+3\right)^2=4[/math] and thought, “There are two numbers, 2 and -2, that equal 4 when squared. This means [math]x+3[/math] is either 2 or it is -2. I can find the values of [math]x[/math] from there.”[/size][br][br]Use Jada’s reasoning to solve the equation.

Can Jada use her reasoning to solve [math]\left(x+3\right)\left(x-3\right)=5[/math]? Explain your reasoning.[br]