[math]40-8=40+n[/math]

[math]25+\text-100=25-n[/math]

[math]3-\frac{1}{2}=3+n[/math]

[math]72-n=72+6[/math]

[size=150]Show that [math]\left(x-1\right)\left(x-1\right)[/math] and [math]x^2-2x+1[/math] are equivalent expressions by drawing a diagram or applying the distributive property. Show your reasoning.[/size][br]

[size=100][size=150]For each expression, write an equivalent expression. Show your reasoning.[br][/size][/size][br][math]\left(x+1\right)\left(x-1\right)[/math]

[math]\left(x-2\right)\left(x+3\right)[/math]

[math](x-2)^2[/math]

[size=150]The quadratic expression [math]x^2+4x+3[/math] is written in [b]standard form[/b].[br][br]Here are some other quadratic expressions. The expressions on the left are written in standard form and the expressions on the right are not.[/size][br][br][table][tr][td]Written in standard form:[/td][td]Not written in standard form:[/td][/tr][tr][td][math]x^2-1[/math][/td][td][math](2x+3)x[/math][/td][/tr][tr][td][math]x^2+9x[/math][/td][td][math]\left(x+1\right)\left(x-1\right)[/math][/td][/tr][tr][td][math]\frac{1}{2}x^2[/math][/td][td][math]3\left(x-2\right)^2+1[/math][/td][/tr][tr][td][math]4x^2-2x+5[/math][/td][td][math]-4\left(x^2+x\right)+7[/math][/td][/tr][tr][td][math]-3x^2-x+6[/math][/td][td][math]\left(x+8\right)\left(-x+5\right)[/math][/td][/tr][tr][td][math]1-x^2[/math][/td][td][/td][/tr][/table][br]What are some characteristics of expressions in standard form?

[math]\left(x+1\right)\left(x-1\right)[/math] and [math]\left(2x+3\right)x[/math] in the right column are quadratic expressions written in [b]factored form[/b]. Why do you think that form is called factored form?[br]

Which quadratic expression can be described as being both standard form and factored form? Explain how you know.