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Alborosie
3 years ago
7

Write an equivalent expression using distributive property and simplify for each question

Mathematics
1 answer:
Lana71 [14]3 years ago
4 0

Answer:

Check explanations

Step-by-step explanation:

For all real numbers a,b, and c, the distributive property states that:

a(b + c) = ab + ac

For Part A, we have

2x + 10x = x(2 + 10) = x(12) = 12x

Or

2x + 10x = 2x(1 + 5) = 2x(6) = 12x

For Part B, we have

-4(3x-10)+5(2-6x)=-4*3x--4*10+5*2-5*6x

This simplifies to:

-4(3x-10)+5(2-6x)=-12x+40+10-30x

-4(3x-10)+5(2-6x)=-12x-30x+40+10

-4(3x-10)+5(2-6x)=-42x+50

For the C part, we have:

2(x - 4) + x = 2 \times x - 2 \times 4 + x

2(x - 4) + x = 2x - 8+ x

2(x - 4) + x = 3x - 8

For Part D, we have:

-3-7(3-4x)+8x =  - 3 - 7 \times 3  - 7 \times  - 4x + 8x

We simplify to get:

-3-7(3-4x)+8x =  - 24+28x + 8x

Simplify further to get:

-3-7(3-4x)+8x =-24+36x

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13/6

Step-by-step explanation:

1 Simplify  \sqrt{8}

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  to  2\sqrt{2}2

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\frac{2}{6\times 2\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})

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\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{9})

12

2

​

2

​

 

2

​

−(−

9

18

​

)

4 Simplify  \frac{18}{9}

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18

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  to  22.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-2)

12

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​

2

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2

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−(−2)

5 Rationalize the denominator: \frac{2}{12\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{2\sqrt{2}}{12\times 2}

12

2

​

2

​

⋅

2

​

2

​

​

=

12×2

2

2

​

​

.

\frac{2\sqrt{2}}{12\times 2}\sqrt{2}-(-2)

12×2

2

2

​

​

 

2

​

−(−2)

6 Simplify  12\times 212×2  to  2424.

\frac{2\sqrt{2}}{24}\sqrt{2}-(-2)

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​

​

 

2

​

−(−2)

7 Simplify  \frac{2\sqrt{2}}{24}

24

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2

​

​

  to  \frac{\sqrt{2}}{12}

12

2

​

​

.

\frac{\sqrt{2}}{12}\sqrt{2}-(-2)

12

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​

 

2

​

−(−2)

8 Use this rule: \frac{a}{b} \times c=\frac{ac}{b}

b

a

​

×c=

b

ac

​

.

\frac{\sqrt{2}\sqrt{2}}{12}-(-2)

12

2

​

 

2

​

​

−(−2)

9 Simplify  \sqrt{2}\sqrt{2}

2

​

 

2

​

  to  \sqrt{4}

4

​

.

\frac{\sqrt{4}}{12}-(-2)

12

4

​

​

−(−2)

10 Since 2\times 2=42×2=4, the square root of 44 is 22.

\frac{2}{12}-(-2)

12

2

​

−(−2)

11 Simplify  \frac{2}{12}

12

2

​

  to  \frac{1}{6}

6

1

​

.

\frac{1}{6}-(-2)

6

1

​

−(−2)

12 Remove parentheses.

\frac{1}{6}+2

6

1

​

+2

13 Simplify.

\frac{13}{6}

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