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malfutka
2 months ago
5

A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored f

orm?
Mathematics
2 answers:
tester [12.3K]2 months ago
7 0
The volume of the cube with a side of 4p is calculated as 4p x 4p x 4p = 64p³

The volume of the cube with a side of 2q² computes to 2q² x 2q² x 2q² = 8q⁶

Total Volume = 64p³ + 8q⁶

Total Volume = (4p)³ + (2q²)³

Total Volume = (4p + 2q²)( (4p)² - (4p)(2q²) + (2q²)²)

Total Volume = (4p + 2q²)( 16p² - 8pq² + 4q⁴)

 
Response:  (4p + 2q²)( 16p² - 8pq² + 4q⁴)
Leona [12.6K]2 months ago
4 0

we understand that

The volume for a cube can be expressed as

V=b^{3}

where

b signifies the side length of the cube

Step 1

Calculate the volume of the cube 1

we have

b=4p\ units

insert into the formula

V1=(4p)^{3}=64p^{3}\ units^{3}

Step 2

Calculate the cube's volume 2

we possess

b=2q^{2}\ units

put into the formula

V2=(2q^{2})^{3}=8q^{6}\ units^{3}

Step 3

Calculate the total volume

Combine volume 1 and volume 2

V=64p^{3}\ units^{3}+8q^{6}\ units^{3}

V=(64p^{3}+8q^{6})\ units^{3}

Step 4

Express the volume in factored form

we know that

The sum of cubes equates to

a^{3} +b^{3} =(a+b)(a^{2} -ab+b^{2})

a=4p\ units

b=2q^{2}\ units

insert

(64p^{3}+8q^{6})=(4p+2q^{2})((4p)^{2}-(4p)(2q^{2})+(2q^{2})^{2}

=(4p+2q^{2})(16p^{2}-8pq^{2}+4q^{4})

thus

the final result is

(4p+2q^{2})(16p^{2}-8pq^{2}+4q^{4})\ units^{3}


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