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1.) 4x^3 + 8x^2y^2 + 12y^3
2.) 5x^3 + 20x^6 + 35x^10
3.)p^2q + pq^2r^2 - pqr + pqr^2

Sagot :

Saitama3idn

Answer:

1.[tex]=4\left(x^3+2x^2y^2+3y^3\right)[/tex]

2.[tex]=20x^6+5x^3[/tex]

3.[tex]=+\cdot \:p\cdot \left(p^2q+pq^2r^2\right)\cdot \:q\cdot \:r^2[/tex]

Step-by-step explanation:

1. Rewrite 12 as [tex]3\cdot \:4[/tex]

Rewrite 8 as [tex]2\cdot \:4[/tex]

[tex]=4x^3+2\cdot \:4x^2y^2+3\cdot \:4y^3[/tex]

Factor out common term 4

[tex]=4\left(x^3+2x^2y^2+3y^3\right)[/tex]

2. Apply rule [tex]a^{1}=a[/tex]

[tex]x^{1} =x[/tex]

[tex]=5x^3+20x^6+35\cdot \:0\cdot \:x[/tex]

Apply rule [tex]0\cdot \:a=0[/tex]

[tex]=5x^3+20x^6+0[/tex]

[tex]5x^3+20x^6+0=5x^3+20x^6[/tex]

[tex]=20x^6+5x^3[/tex]

3.Find Least Common Multiplier of [tex]p^2q\:+\:pq^2r^2\:-\:pqr\:+\:pqr^2[/tex]

Lowest Common Multiplier (LCM)

The LCM of a, b is the smallest multiplier that is duvisible by both a and b

Factor [tex]+pqr^2[/tex]

[tex]p^2q\:+\:pq^2r^2\:-\:pqr\:+\:pqr^2[/tex]

Multiply each factor with the highest power:

[tex]p^2q\:+\:pq^2r^2\:-\:pqr\:+\:pqr^2[/tex]

I hope this is helpful :)

SAITAMA!!

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