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Solution 2.1:2a

From Förberedande kurs i matematik 1

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(Ny sida: {{NAVCONTENT_START}} <center> Bild:2_1_2a.gif </center> {{NAVCONTENT_STOP}})
Current revision (08:10, 23 September 2008) (edit) (undo)
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First, multiply the brackets together. In the first product, every term in the first bracket is multiplied by every term in the second bracket,
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<center> [[Bild:2_1_2a.gif]] </center>
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{{NAVCONTENT_STOP}}
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{{Displayed math||<math>\begin{align}
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(x-4)(x-5)-3x(2x-3)&= x\cdot x-x\cdot 5- 4\cdot x-4\cdot (-5)-(3x \cdot 2x-3x\cdot 3)\\
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&= x^2-5x-4x+20-(6x^2-9x)\\
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&=x^2-5x-4x+20-6x^2+9x\,\textrm{.}
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\end{align}</math>}}
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Then, gather together ''x''²-, ''x''- and the constant terms and simplify
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{{Displayed math||<math>\begin{align}
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\phantom{(x-4)(x-5)-3x(2x-3)}&= (x^2-6x^2)+(-5x-4x+9x)+20 \\
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&= -5x^2+0+20\\
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&= \rlap{-5x^2+20\,\textrm{.}}\phantom{x\cdot x-x\cdot 5- 4\cdot x-4\cdot (-5)-(3x \cdot 2x-3x\cdot 3)}
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\end{align}</math>}}

Current revision

First, multiply the brackets together. In the first product, every term in the first bracket is multiplied by every term in the second bracket,

(x4)(x5)3x(2x3)=xxx54x4(5)(3x2x3x3)=x25x4x+20(6x29x)=x25x4x+206x2+9x.

Then, gather together x²-, x- and the constant terms and simplify

=(x26x2)+(5x4x+9x)+20=5x2+0+20=5x2+20.