Go through the **Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.4 Equivalent Expressions**and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 5 Lesson 5.4 Equivalent Expressions Answers Key

Equivalent expressions are created by simplifying values and combining terms.

4(6x – 5) = 24x – 20 Multiply each value by 4 to create an equivalent expression.

3(4^{3} + 7x) = 3(64 + 7x) First, calculate the value of the exponents.

3(64 + 7x) = 192 + 21x Then, use the distributive property to create the equivalent expression.

t + t + t = 3t Use multiplication in place of repeated addition.

**Create expressions equivalent to the ones below.**

Question 1.

7(4z + 8b) ____________

Answer:

Given term is 7(4z + 8b)

Multiply the every given term with 7 as shown below

= 7x 4z + 1 x 8b

= 28z + 8b

Hence the Equivalent Expression for 7(4z + 8b) is 28z + 8b.

Question 2.

8(2x + 3^{2}) ____________

Answer:

Given term is 8(2x + 3^{2})

1. First calculate the Exponent value of 3^{2} = 9

= 8(2x + 9)

2. Multiply the every given term with 8 as shown below

= 8(2x)+ 8(9)

= 16x + 72

Hence the Equivalent Expression for 8(2x + 3^{2}) is 16x + 72.

Question 3.

4(r + r + r + r) ____________

Answer:

Given term is 4(r + r + r + r)

Multiply the every given term with 4 as shown below

= 4r + 4r + 4r + 4r

= 16r

Hence the Equivalent Expression for 4(r + r + r + r) is 16r.

Question 4.

9(3 + 8x) ____________

Answer:

Given term is 9(3 + 8x)

Multiply the every given term with 9 as shown below

= 9(3) + 9(8x)

= 27 + 72x

Hence the Equivalent Expression for 9(3 + 8x) is27 + 72x.

Question 5.

4^{2}(3 + 6t) ________

Answer:

Given term is 8(2x + 3^{2})

1. First calculate the Exponent value of 4^{2} = 16

= 16(3 + 6t)

2. Multiply the every given term with 16 as shown below

= 16 x 3+ 16 x 16t

= 48 + 256t

Hence the Equivalent Expression for 4^{2}(3 + 6t) is 48 + 256t.

Question 6.

\(\frac{t+t+t}{4}\) ____________

Answer:

Given term \(\frac{t+t+t}{4}\)

Add the given 3 literals then the result obtained is 3t

Then , substitute the 3t i.e. \(\frac{3t}{4}\).

Therefore the \(\frac{t+t+t}{4}\) value is \(\frac{3t}{4}\).

Question 7.

2(4s^{3} + 2) ________

Answer:

Given term is 2(4s^{3} + 2)

Multiply the every given term with 16 as shown below

= 2 x 4s^{3} + 2 x 2

= 8s^{3} + 4

Hence the Equivalent Expression for 2(4s^{3} + 2) is 8s^{3} + 4.

Question 8.

30(3x + 4) ____________

Answer:

Given term is 30(3x + 4)

Multiply the every given term with 30 as shown below

= (30).(3x) +(30).(4)

= 90x + 120

Hence the Equivalent Expression for 30(3x + 4) is 90x + 120.

Question 9.

6(5a + 9b) ________

Answer:

Given term is 6(5a + 9b)

Multiply the every given term with 6 as shown below

= 6 x 5a +6 x 9b

= 30a + 54b

Hence the Equivalent Expression for 6(5a + 9b) is 30a + 54b.

Question 10.

9(3x + 5^{4}) ________

Answer:

Given term is 9(3x + 5^{4})

1. First calculate the Exponent value of 5^{4} = 625

= 9(3x +625)

2. Multiply the every given term with 6 as shown below

= (9).(3x) + 9.(625)

= 27x + 5625

Hence the Equivalent Expression for 9(3x + 5^{4}) is 27x + 5625.

Question 11.

7(c + c + c) ________

Answer:

Given term is 7(c + c + c)

Multiply the every given term with 7 as shown below

= 7c + 7c + 7c

= 21c

Hence the Equivalent Expression for 7(c + c + c) is 21c.

Question 12.

9(2 + 7f) _________________

Answer:

Given term is 9(2 + 7f)

Multiply the every given term with 9 as shown below

= (9. 2) + (9.7f)

= 18 + 63f

Hence the Equivalent Expression for 9(2 + 7f) is 18 + 63f.

Question 13.

7^{5}(4g – 8d) ________

Answer:

Given term is 7^{5}(4g – 8d)

1. First calculate the Exponent value of 7^{5} = 16807

2. Multiply the every given term with 16807 as shown below

= (16807).(4g) + 16807.(8d)

= 67228 g +134456d

Hence the Equivalent Expression for 7^{5}(4g – 8d) is 67228 g +134456d.

Question 14.

\(\frac{e+e+e}{5}\) ____________

Answer:

Given term \(\frac{e+e+e}{5}\)

Add the given three e literals the result obtained is 3e

Then , substitute the 3e in \(\frac{e+e+e}{5}\)

Therefore the \(\frac{e+e+e}{5}\) value is \(\frac{3e}{5}\).

Question 15.

5(3z^{6} + 3) _____

Answer:

Given term is 5(3z^{6} + 3)

Multiply the every given term with 5 as shown below

= 5 x 3z^{6} + 5 x3.

= 15 z^{6}+ 15

Hence the Equivalent Expression for 5(3z^{6} + 3) is15 z^{6}+ 15.

Question 16.

10(y + 2) _________

Answer:

Given term is 10(y + 2)

Multiply the every given term with 10 as shown below

= (10).(y) + (10.2)

= 10y+ 20

Hence the Equivalent Expression for10(y + 2) is 10y+ 20.

**Create expressions equivalent to the ones below.**

Question 1.

4(a + b) _________________

Answer:

Given term is 4(a + b)

Multiply the every given term with 4 as shown below

= (4).(a) + (4.b)

= 4a+ 4b

Hence the Equivalent Expression for 4(a + b) is 4a+4.

Question 2.

3(9a + 8b) ____________

Answer:

Given term is 3(9a + 8b)

Multiply the every given term with 3 as shown below

= (3).(9a) + (3.8b)

= 27a+ 24b

Hence the Equivalent Expression for3(9a + 8b) is 27a+ 24b.

Question 3.

9(x + 2y) ____________

Answer:

Given term is 9(x + 2y)

Multiply the every given term with 9 as shown below

= (9).(x) + (9).(2y)

= 9x+ 2y

Hence the Equivalent Expression for9(x + 2y) is 9x+ 2y.

Question 4.

2(9x + 3^{2}) ____________

Answer:

Given term is 2(9x + 3^{2})

1. First calculate the Exponent value of 3^{2}= 9

Then 2(9x + 3^{2}) = 2(9x+ 9)

2. Multiply the every given term with 2 as shown below

= (2).(9x) + 2.(9)

= 18x +18

Hence the Equivalent Expression for 2(9x + 3^{2})is18x +18.

Question 5.

5^{3}(2 + 4c) ____________

Answer:

Given term is 5^{3}(2 + 4c)

1. First calculate the Exponent value of 5^{3}= 125

Then 5^{3}(2 + 4c)= 125(2+ 4c)

2. Multiply the every given term with 125 as shown below

= (125).(2) + (125).(4c)

= 250 +500c

Hence the Equivalent Expression for 5^{3}(2 + 4c) is 250 +500c.

Question 6.

\(\frac{x+x}{3}\) ____________

Answer:

Given term \(\frac{x+x}{3}\)

First Add the given two x literals the result obtained is 2x

Then, substitute the 2x in \(\frac{2x}{3}\)

Therefore the \(\frac{x+x}{3}\) value is \(\frac{2x}{3}\)

Question 7.

4^{2}( 12 + 5c) _________

Answer:

Given term is 4^{2}( 12 + 5c)

1. First calculate the Exponent value of 4^{2}= 16

Then 4^{2}( 12 + 5c) = 16(12+ 5c)

2. Multiply the every given term with 16 as shown below

= (16).(12) + (16).(5c)

= 192 + 80c

Hence the Equivalent Expression for 4^{2}( 12 + 5c) is 192 + 80c.

Question 8.

17(14r + 3^{3}) – 7r ________

Answer:

Given term is 17(14r + 3^{3}) – 7r

1. First calculate the Exponent value of 3^{3}= 27

Then 17(14r + 3^{3}) – 7r = 17(14r + 27) – 7r

2. Multiply the every given term with 17 as shown below

= (17).(14r) + (17).(27) – 17r

= 238r + 459 – 17r

= 221r + 459

Hence the Equivalent Expression for 17(14r + 3^{3}) – 7r is 221r + 459.

Question 9.

6(c – f) ____________

Answer:

Given term is 6(c – f)

Multiply the every given term with 6 as shown below

= (6).(c) + (6).(f)

= 6c -6f

Hence the Equivalent Expression for 6(c – f) is 6c -6f .

Question 10.

4(10b – 10c) _______________

Answer:

Given term is 4(10b – 10c)

Multiply the every given term with 4 as shown below

= (4).(10b) – (4).(10c)

= 40b – 40c

Hence the Equivalent Expression for 4(10b – 10c) is 40b – 40c .

Question 11.

8(g – 3d) _________

Answer:

Given term is 8(g – 3d)

Multiply the every given term with 8 as shown below

= (8).(g) + (8).(3d)

= 8g -24d

Hence the Equivalent Expression for 8(g – 3d) is 8g -24g.

Question 12.

3(7h + 4^{2}) __________

Answer:

Given term is 3(7h + 4^{2})

1. First calculate the Exponent value of 4^{2}= 16

Then 3(7h + 4^{2}) = 3(7h + 16)

2. Multiply the every given term with 3 as shown below

= (3).(7h) + (3).(16)

= 21h + 48

Hence the Equivalent Expression for 3(7h + 4^{2}) is 21h + 48.

Question 13.

4^{5}(3 + 5t) ________

Answer:

Given term is 3(7h + 4^{2})

1. First calculate the Exponent value of 4^{5 }= 1024

Then 4^{5}(3 + 5t) = 1024

2. Multiply the every given term with 1024 as shown below

= ().(3) + ().(5t)

= 3072 + 5120t

Hence the Equivalent Expression for 4^{5}(3 + 5t) is 3072 + 5120t.

Question 14.

\(\frac{d+d}{10}\) ____________

Answer:

Given term \(\frac{d+d}{10}\)

First Add the given two d literals which gives as 2d

Then substitute the 2d i.e. \(\frac{2d}{10}\)

\(\frac{d}{5}\)

Therefore the \(\frac{d+ d}{10}\) value is \(\frac{d}{5}\).

Question 15.

6^{4}(25 + t) ________

Answer:

Given term is 6^{4}(25 + t)

1. First calculate the Exponent value of 6^{4 }= 1296

Then 6^{4}(25 + t) = 1296(25 + t)

2. Multiply the every given term with 1296 as shown below

= (1296).(25) + (1296).(t)

= 32400 + 1296t

Hence the Equivalent Expression for 6^{4}(25 + t) is 32400 + 1296t.

Question 16.

19(20f – w^{4}) + 3f _______________

Answer:

Given term is 19(20f – w^{4}) + 3f

Multiply the given term19(20f – w^{4}) with 19 as shown below

= (19).(20f)- (19).(w^{4})+ 3f

= 380f – 19w^{4} + 3f

Hence the Equivalent Expression for19(20f – w^{4}) + 3f is 380f – 19w^{4} + 3f.