Show the ((x-1)(x-1)) and (x^2 - 2x + 1) are equivalent expressions by illustration a diagram or applying the distributive property. Show your reasoning.For every expression, write an tantamount expression. Present your reasoning.((x+1)(x-1))((x-2)(x+3))((x-2)^2)

The quadratic expression (x^2 + 4x + 3) is written in standard form.

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Here room some other quadratic expressions. The expression on the left room written in standard kind and the expression on the ideal are not.


Written in traditional form:

(x^2 – 1)

( x^2 + 9x)

(frac12 x^2)

(4x^2 – 2x + 5)

( ext-3x^2 – x + 6)

(1 - x^2)


Not composed in standard form:

((2x + 3)x)

((x+1)(x-1))

(3(x-2)^2 +1)

( ext-4(x^2 + x) +7)

( (x+8)( ext-x+5))


What room some characteristics of expression in typical form?((x+1)(x-1)) and also ((2x + 3)x) in the right pillar are quadratic expressions written in factored form. Why execute you think that kind is called factored form?
Which quadratic expression can be described as being both standard form and factored form? define how girlfriend know.


A quadratic role can regularly be represented by many equivalent expressions. Because that example, a quadratic role (f) might be defined by (f(x) = x^2 + 3x + 2). The quadratic expression (x^2 + 3x + 2) is dubbed the standard form, the amount of a lot of of (x^2) and also a linear expression ((3x+2) in this case).

In general, standard form is (displaystyle ax^2 + bx + c) 

We refer to (a) as the coefficient of the squared hatchet (x^2), (b) together the coefficient the the linear term (x), and (c) together the continuous term.

The duty (f) can likewise be characterized by the equivalent expression ((x+2)(x+1)). When the quadratic expression is a product the two components where every one is a direct expression, this is referred to as the factored form.

An expression in factored type can be rewritten in standard type by expanding it, which means multiplying the end the factors. In a vault lesson us saw exactly how to use a diagram and also to use the distributive residential property to multiply two direct expressions, such together ((x+3)(x+2)). We deserve to do the exact same to expand an expression through a sum and a difference, such as ((x+5)(x-2)), or to expand an expression with two differences, because that example, ((x-4)(x-1)).

To represent ((x-4)(x-1)) through a diagram, we can think of subtraction as adding the opposite:


(x)( ext-4)(x)( ext-1)
(x^2)( ext-4x)
( ext-x)(4)


Description: Diagram mirroring distributive property.

 

Row 1: x minus 4 trebab.netes x minus 1.

 

Row 2: equates to x plus an unfavorable 4 trebab.netes x plus negative 1. Two arrows attracted from both an initial x and also from an unfavorable 4, because that each, one arrow to the second x, one arrowhead to an unfavorable 1.

 

Row 3: amounts to x trebab.netes the quantity x plus negative one, plus negative 4 trebab.netes the amount x plus an unfavorable 1. 2 arrows attracted from very first x to second x and an adverse 1. 2 arrows drawn from an adverse 4 to 3rd x and an unfavorable 1.

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Row 4: equals x squared plus an unfavorable 1 x plus negative 4 x plus an adverse 4 trebab.netes an adverse 1.