exponentiation of algebraic expressions

( O P E RA S I P E M A N G KATA N B E N T U K A L JA B A R )

EXPONENTIATION OF ALGEBRAIC

EXPRESSIONS

REMEMBER

• that’s mean 2x2x2• that’s mean 3x3

So ………..• that’s mean xxx• ()that’s mean () x () =

be careful :• (- 2 ‡ - (2 ) because

(- 2 = 4 and - (2 ) = - 4

REMEMBER OF PROPERTIES OF EXPONENTIATION

•()³ = •()³ =

EXCERCISESFind the exponentiation products of the

following algebraic expression(Tentukanhasiloperasipangkatdaribentukaljab

arberikutini)1. ()³ =………2. - ( 2)² = …….3.( - 3 )² =………4. (- 4)³ =………5. - ( 2)² =………..6. (- )² =………..

SOLUTION

1. ()³ =………

(3)³ x ()³ = 27

Can you do like that example with others exercises ?please do it……..

(kalau belajarnya sedikit-sedikit, kalau rajin, kalau tekun dan sering latihan……)

BAGAIMANA ? MATEMATIKA ITU MUDAH KAN ?

NOW, LET’S DISCUSS ABOUT :

• Exponentiation of Two Terms (binomial)(OperasiPemangkatanSukuDua )

Examples :1). ( a + b )² = (a + b)(a + b) = 2) (a – b )² = ( a - b )(a – b ) =

• And then…...3) ( a + b )³ = ( a + b)(a + b )( a + b )=() )( a + b )= a³ + + + ² + ² + b³= a³ + 3 + 3 ² + b³

4) ( = + 4 + 6 +

5) = + 5 10 + 10 + 5 +

LOOK AT THE EXPONENTIATION PRODUCTS ABOVE

• Exponent a from the left to the right decreases by 1

and ( pangkat dari a menurun mulai dari kiri ke kanan)• Exponent b from the left to the right increases by

1( pangkat dari b bertambah/ naik mulai dari kiri ke kanan

PASCAL’S TRIANGLE

LOOK AT PASCAL’S TRIANGLE ABOVE

• The coefficients of the terms of exponentiation products are called BINOMIAL COEFFICIENTS and can be determined by Pascal’s Triangle.• Example : = 1 1 = + 1…….1 = + 2 + 1…2…1And so on………

EXERCISES

1. Find the exponentiation products of the following algebraic expressions :• a). b) c)) d)2. Expand and simplify

SOLUTION

• 1 a) ). =

• 2 a). = )() = . + . + . + . = + + + 25 = + + 25

DO IT BY YOURSELF

• But you must ask someone if you still confused• Berusahalah agar kalian…..

KARENA…..

• Math is magic

BUKU SUMBER

• Pelajaran MATEMATIKA BILINGUAL• Untuk SMP/MTs• Penulis : - Cucun Cunayah- Ahmad Zaelani- Suwah Seembiring

•Copyright 2010 pada CV YRAMA WIDYA

TERIMA KASIH…..THANK YOU…..

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