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Math 8 Enhancement Activity.docx
1.
Directions: Write the
Rational Algebraic Expressions in simplest form. Given Solution Scratch 1.) 24𝑚2𝑝2 36𝑚𝑝2 = 𝟏𝟐𝒎𝒑𝟐(2𝑚) 𝟏𝟐𝒎𝒑𝟐(3) Numerator 24𝑚2 𝑝3 = (2) (2) (2) (3) (m) (m) (p) (p) Denominator 36𝑚 𝑝3 = (2) (2) (3) (3) (m) (p) (P) GCMF = (2) (2) (3) (m) (p) (p) = 𝟏𝟐𝒎𝒑𝟐 = 𝟏𝟐𝒎𝒑𝟐(2𝑚) 𝟏𝟐𝒎𝒑𝟐(3) Simplified Form = 2𝑚 3 2.) 4𝑏𝑝2+6𝑏2𝑝 6𝑝2+2𝑝 = 𝟐𝒃𝒑(𝟐𝒑 +𝟑𝒃) 𝟐𝒑(𝟑𝒑 +𝟏) Numerator 4𝑏𝑝2 = (2) (2) b (p) (p) 6𝑏2 𝑝 = (2) (3) (b) (b) (p) GCMF = (2) (b) (p) = 𝟐𝒃𝒑 Factored Form of the Numerator = 𝟐𝒃𝒑(2p +3b) = 𝟐𝒃𝒑(𝟐𝒑 +𝟑𝒃) 𝟐𝒑(𝟑𝒑 +𝟏) Simplified Form = 𝒃(𝟐𝒑 +𝟑𝒃) (𝟑𝒑 +𝟏) Denominator 6𝑝2 = (2) (3) (p) (p) 2𝑝 = (2) (p) GCMF = (2) (p) = 𝟐𝒑 Factored Form of the Numerator = 𝟐𝒑(3p +1)
2.
Given Solution Scratch 3.) 4𝑟2−
9𝑐2 8𝑟3+ 27𝑐3 = (𝟐𝒓+𝟑𝒄)(2𝑟−3𝑐) (2𝑟+3𝑐 )( 4𝑟2 – 6𝑟𝑐+9𝑐2) Numerator Difference of Two Squares Formula 𝑎2 − 𝑏2 = (𝑎 + 𝑏)(𝑎 − 𝑏) 4𝑟2 − 9𝑐2 = (2𝑟 + 3𝑐)(2𝑟 − 3𝑐) (2𝑟)(2𝑟) (3𝑐)(3𝑐) 𝒂 𝒃 Denominator Sum of Two Cubes 8𝑟3 + 27𝑐3 = (2𝑟)3 + (3𝑐)3 (2r)(2𝑟)(2𝑟) (3𝑐)(3𝑐)(3𝑐) 𝒇𝒊𝒓𝒔𝒕 𝒃𝒂𝒔𝒆 𝒔𝒆𝒄𝒐𝒏𝒅 𝒃𝒂𝒔𝒆 = (2𝑟 3𝑐 )( ) = (2𝑟 3𝑐 )( 2𝑟.2𝑟 ) = (2𝑟 3𝑐 )( 4𝑟2 ) = (2𝑟 3𝑐 )( 4𝑟2 2𝑟. 3𝑐 ) = (2𝑟 3𝑐 )( 4𝑟2 6𝑟𝑐 ) = (2𝑟 3𝑐 )( 4𝑟2 6𝑟𝑐 3𝑐. 3𝑐) ) = (2𝑟 3𝑐 )( 4𝑟2 6𝑟𝑐 9𝑐2 ) = (2𝑟 + 3𝑐 )( 4𝑟2 – 6𝑟𝑐 + 9𝑐2 ) S O AP = (𝟐𝒓+𝟑𝒄)(2𝑟−3𝑐) (2𝑟+3𝑐 )( 4𝑟2 – 6𝑟𝑐+9𝑐2) Simplified Form = 2𝑟−3𝑐 4𝑟2 – 6𝑟𝑐+9𝑐2
3.
Given Solution Scratch 4.) 4𝑑2+2𝑑−
6 2𝑑2+5𝑑+ 3 = (2𝑑+3)(2𝑑−2) (2𝑑+3)(𝑑+1) Numerator Trinomial (2𝑑 + 3) (2𝑑 − 2) Factors of the Trinomial (2𝑑 + 3)(2𝑑 − 2) Denominator Trinomial (2𝑑 + 3) (𝑑 + 1) Factors of the Trinomial (2𝑑 + 3)(𝑑 + 1) = (2𝑑+3)(2𝑑−2) (2𝑑+3)(𝑑+1) Simplified Form = 2𝑑−2 𝑑+1
4.
Given Solution Scratch 5.) 2𝑑−
6 6 − 2𝑑 = (2𝑑−6) −1(2𝑑−6) Retain Numerator 2𝑑 − 6 Change the Denominator 6 − 2𝑑 a. 2𝑑 6 b. 2𝑑 − 6 c. −1(2𝑑 − 6) = (2𝑑−6) −1(2𝑑−6) Simplified Form = 1 −1 = −1
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