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1Simplify \(8k^2 + 4k^2\).
Answer
\(8k^2 + 4k^2 = 12k^2\)
Simplify \(2y^2 + 6y^2 + 14y – 7y + 7\).
Answer
\(2y^2 + 6y^2 + 14y – 7y + 7 \\ \, \\ = \underbrace{(2y^2 + 6y^2)}_{\text{Like-Terms}} + \underbrace{(14y – 7y)}_{\text{Like-Terms}} + 7 \\ \, \\ = 8y^2 + 7y + 7 \)
Simplify \(\dfrac{15a+5b}{3a+b}\).
Answer
\(\require{cancel} \dfrac{15a+5b}{3a+b} \\ \, \\ =\dfrac{5(3a+b)}{3a+b} \\ \, \\ = \dfrac{5\cancel{({\color{red}{3a+b}})}}{\cancel{{\color{red}{3a+b}}}} \\ \, \\ = 5 \)
Simplify \(\dfrac{9x+27}{3\sqrt{3}}\).
Answer
\(\require{cancel} \dfrac{9x+27}{3\sqrt{3}} \\ \, \\ =\dfrac{9(x+3)}{3\sqrt{3}} \\ \, \\ =\dfrac{9(x+3)}{3\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}} \\ \, \\ =\dfrac{9\sqrt{3}(x+3)}{3\cdot3} \\ \, \\ =\dfrac{9\sqrt{3}(x+3)}{9} \\ \, \\ =\dfrac{\cancel{{\color{red}{9}}}\sqrt{3}(x+3)}{\cancel{{\color{red}{9}}}} \\ \, \\ = \sqrt{3}(x+3)\)
Simplify \(\dfrac{8y+24}{\sqrt{8}}\).
Answer
\(\require{cancel} \dfrac{8y+24}{\sqrt{8}} \\ \, \\ =\dfrac{8(y+3)}{\sqrt{8}} \\ \, \\ =\dfrac{8(y+3)}{\sqrt{8}}\cdot\dfrac{\sqrt{8}}{\sqrt{8}} \\ \, \\ =\dfrac{8\sqrt{8}(y+3)}{8} \\ \, \\ =\dfrac{\cancel{{\color{red}{8}}}\sqrt{8}(y+3)}{\cancel{{\color{red}{8}}}} \\ \, \\ =\sqrt{8}(y+3) \\ \, \\ =\sqrt{4\times2}(y+3) \\ \, \\ =2\sqrt{2}(y+3)\)