quentinanton
Answered

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Factor completely .
4u^2 - 100

Factor Completely 4u2 100 class=

Sagot :

jacob193

Answer:

[tex]4\, (u + 5)\, (u - 5)[/tex].

Step-by-step explanation:

Make use of the fact that the difference of two perfect squares, [tex](x^{2} - y^{2})[/tex], could be rewritten as a product of the form [tex](x + y)\, (x - y)[/tex]. That is:

[tex]x^{2} - y^{2} = (x + y)\, (x - y)[/tex].

In this question, the two squares are [tex](2\, u)^{2}[/tex] and [tex]10^{2}[/tex], respectively. Thus:

[tex]\begin{aligned}& 4\, u^{2} - 100 \\=\; & (2\, u)^{2} - (10)^{2} \\ =\; & (2\, u + 10) \, (2\, u - 10) \end{aligned}[/tex].

Simplify this expression even further:

[tex]\begin{aligned} & (2\, u + 10) \, (2\, u - 10) \\ =\; & (2\, (u + 5))\, (2\, (u - 5)) \\ =\; & 4\, (u + 5)\, (u - 5)\end{aligned}[/tex].

StayAliveFren

Answer:

4(u - 5)(u + 5)

Step-by-step explanation:

We have the expression, [tex]4u^2-100[/tex]

Factor out 4: [tex]4(u^2-25)[/tex]

25 can be written as [tex]5^2[/tex]

Use difference of squares property: [tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex]4(u^2-5^2)[/tex]

= [tex]4(u-5)(u+5)[/tex]

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