Answered

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Expand and simplify:
a) -1/3{6(p+q)-3[p-2(p-3q)]}
A=-3p+4q

b) y-2/3(9x-3y)
A=-6x+3y

(The answer is written at the back of our books but I am struggling with the working I mean how to achieve the answer?)

Sagot :

sqdancefan

Answer:

  a) -3p +4q

  b) -6x +3y

Step-by-step explanation:

Use the distributive property to eliminate parentheses. Use the properties of arithmetic to combine the numbers.

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a)

The order of operations tells you to start with the inner parentheses and work outward.

  [tex]-\dfrac{1}{3}(6(p+q)-3(p-2(p-3q)))=-\dfrac{1}{3}(6(p+q)-3(p+(-2)(p) +(-2)(-3q)))\\\\=-\dfrac{1}{3}(6(p+q)-3(p-2p+6q))=-\dfrac{1}{3}(6(p+q)-3(-p+6q))\\\\=-\dfrac{1}{3}((6)(p)+(6)(q)+(-3)(-p)+(-3)(6q))=-\dfrac{1}{3}(6p+6q+3p-18q)\\\\=-\dfrac{1}{3}(9p -12q)=(-\dfrac{9p}{3})+(-\dfrac{-12q}{3})=\boxed{-3p+4q}[/tex]

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b)

Same deal for the second expression: use the distributive property and combine like terms.

  [tex]y-\dfrac{2}{3}(9x-3y)=y+(-\dfrac{2\cdot9x}{3})+(-\dfrac{2(-3y)}{3})\\\\=y-6x+2y=\boxed{-6x+3y}[/tex]

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