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# Math 8 Enhancement Activity.docx

23. Mar 2023โขโข
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### Math 8 Enhancement Activity.docx

1. Directions: Write the Rational Algebraic Expressions in simplest form. Given Solution Scratch 1.) 24๐2๐2 36๐๐2 = ๐๐๐๐๐(2๐) ๐๐๐๐๐(3) Numerator 24๐2 ๐3 = (2) (2) (2) (3) (m) (m) (p) (p) Denominator 36๐ ๐3 = (2) (2) (3) (3) (m) (p) (P) GCMF = (2) (2) (3) (m) (p) (p) = ๐๐๐๐๐ = ๐๐๐๐๐(2๐) ๐๐๐๐๐(3) Simplified Form = 2๐ 3 2.) 4๐๐2+6๐2๐ 6๐2+2๐ = ๐๐๐(๐๐ +๐๐) ๐๐(๐๐ +๐) Numerator 4๐๐2 = (2) (2) b (p) (p) 6๐2 ๐ = (2) (3) (b) (b) (p) GCMF = (2) (b) (p) = ๐๐๐ Factored Form of the Numerator = ๐๐๐(2p +3b) = ๐๐๐(๐๐ +๐๐) ๐๐(๐๐ +๐) Simplified Form = ๐(๐๐ +๐๐) (๐๐ +๐) Denominator 6๐2 = (2) (3) (p) (p) 2๐ = (2) (p) GCMF = (2) (p) = ๐๐ Factored Form of the Numerator = ๐๐(3p +1)
2. Given Solution Scratch 3.) 4๐2โ 9๐2 8๐3+ 27๐3 = (๐๐+๐๐)(2๐โ3๐) (2๐+3๐ )( 4๐2 โ 6๐๐+9๐2) Numerator Difference of Two Squares Formula ๐2 โ ๐2 = (๐ + ๐)(๐ โ ๐) 4๐2 โ 9๐2 = (2๐ + 3๐)(2๐ โ 3๐) (2๐)(2๐) (3๐)(3๐) ๐ ๐ Denominator Sum of Two Cubes 8๐3 + 27๐3 = (2๐)3 + (3๐)3 (2r)(2๐)(2๐) (3๐)(3๐)(3๐) ๐๐๐๐๐ ๐๐๐๐ ๐๐๐๐๐๐ ๐๐๐๐ = (2๐ 3๐ )( ) = (2๐ 3๐ )( 2๐.2๐ ) = (2๐ 3๐ )( 4๐2 ) = (2๐ 3๐ )( 4๐2 2๐. 3๐ ) = (2๐ 3๐ )( 4๐2 6๐๐ ) = (2๐ 3๐ )( 4๐2 6๐๐ 3๐. 3๐) ) = (2๐ 3๐ )( 4๐2 6๐๐ 9๐2 ) = (2๐ + 3๐ )( 4๐2 โ 6๐๐ + 9๐2 ) S O AP = (๐๐+๐๐)(2๐โ3๐) (2๐+3๐ )( 4๐2 โ 6๐๐+9๐2) Simplified Form = 2๐โ3๐ 4๐2 โ 6๐๐+9๐2
3. Given Solution Scratch 4.) 4๐2+2๐โ 6 2๐2+5๐+ 3 = (2๐+3)(2๐โ2) (2๐+3)(๐+1) Numerator Trinomial (2๐ + 3) (2๐ โ 2) Factors of the Trinomial (2๐ + 3)(2๐ โ 2) Denominator Trinomial (2๐ + 3) (๐ + 1) Factors of the Trinomial (2๐ + 3)(๐ + 1) = (2๐+3)(2๐โ2) (2๐+3)(๐+1) Simplified Form = 2๐โ2 ๐+1
4. Given Solution Scratch 5.) 2๐โ 6 6 โ 2๐ = (2๐โ6) โ1(2๐โ6) Retain Numerator 2๐ โ 6 Change the Denominator 6 โ 2๐ a. 2๐ 6 b. 2๐ โ 6 c. โ1(2๐ โ 6) = (2๐โ6) โ1(2๐โ6) Simplified Form = 1 โ1 = โ1
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