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ACTIVITY 5 : Factoring Sum and Difference of Two Cubes

Factor out theeach binomial completely.

7.) a³b³ - y³
8.) 24 + 54c³
9.) 1|8x3 - 216
10.) 343a⁶ + 1|27y⁹

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ACTIVITY 5 Factoring Sum And Difference Of Two CubesFactor Out Theeach Binomial Completely7 Ab Y8 24 54c9 18x3 21610 343a 127yclick The Photo Para Po Maliinawan class=

Sagot :

ALMONDS1IN

Answer:

1.1 Factoring: a3b3-y3

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0-b3 =

a3-b3

Check : a3 is the cube of a1

Check : b3 is the cube of b1

Check : y3 is the cube of y1

Factorization is :

(ab - y) • (a2b2 + aby + y2)

Trying to factor a multi variable polynomial :

1.2 Factoring a2b2 + aby + y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

(ab - y) • (a2b2 + aby + y2)

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