### Math 8 Enhancement Activity.docx

1. Directions: Write the Rational Algebraic Expressions in simplest form. Given Solution Scratch 1.) 24π2π2 36ππ2 = πππππ(2π) πππππ(3) Numerator 24π2 π3 = (2) (2) (2) (3) (m) (m) (p) (p) Denominator 36π π3 = (2) (2) (3) (3) (m) (p) (P) GCMF = (2) (2) (3) (m) (p) (p) = πππππ = πππππ(2π) πππππ(3) Simplified Form = 2π 3 2.) 4ππ2+6π2π 6π2+2π = πππ(ππ +ππ) ππ(ππ +π) Numerator 4ππ2 = (2) (2) b (p) (p) 6π2 π = (2) (3) (b) (b) (p) GCMF = (2) (b) (p) = πππ Factored Form of the Numerator = πππ(2p +3b) = πππ(ππ +ππ) ππ(ππ +π) Simplified Form = π(ππ +ππ) (ππ +π) Denominator 6π2 = (2) (3) (p) (p) 2π = (2) (p) GCMF = (2) (p) = ππ Factored Form of the Numerator = ππ(3p +1)
2. Given Solution Scratch 3.) 4π2β 9π2 8π3+ 27π3 = (ππ+ππ)(2πβ3π) (2π+3π )( 4π2 β 6ππ+9π2) Numerator Difference of Two Squares Formula π2 β π2 = (π + π)(π β π) 4π2 β 9π2 = (2π + 3π)(2π β 3π) (2π)(2π) (3π)(3π) π π Denominator Sum of Two Cubes 8π3 + 27π3 = (2π)3 + (3π)3 (2r)(2π)(2π) (3π)(3π)(3π) πππππ ππππ ππππππ ππππ = (2π 3π )( ) = (2π 3π )( 2π.2π ) = (2π 3π )( 4π2 ) = (2π 3π )( 4π2 2π. 3π ) = (2π 3π )( 4π2 6ππ ) = (2π 3π )( 4π2 6ππ 3π. 3π) ) = (2π 3π )( 4π2 6ππ 9π2 ) = (2π + 3π )( 4π2 β 6ππ + 9π2 ) S O AP = (ππ+ππ)(2πβ3π) (2π+3π )( 4π2 β 6ππ+9π2) Simplified Form = 2πβ3π 4π2 β 6ππ+9π2
3. Given Solution Scratch 4.) 4π2+2πβ 6 2π2+5π+ 3 = (2π+3)(2πβ2) (2π+3)(π+1) Numerator Trinomial (2π + 3) (2π β 2) Factors of the Trinomial (2π + 3)(2π β 2) Denominator Trinomial (2π + 3) (π + 1) Factors of the Trinomial (2π + 3)(π + 1) = (2π+3)(2πβ2) (2π+3)(π+1) Simplified Form = 2πβ2 π+1
4. Given Solution Scratch 5.) 2πβ 6 6 β 2π = (2πβ6) β1(2πβ6) Retain Numerator 2π β 6 Change the Denominator 6 β 2π a. 2π 6 b. 2π β 6 c. β1(2π β 6) = (2πβ6) β1(2πβ6) Simplified Form = 1 β1 = β1