Question

Use the identity below to complete the tasks: a3 + b3 = (a + b)(a2 - ab + b2) Use the identity for the sum of two cubes to factor 8q6r3 + 27s6t3. What is a? What is b? Factor the expression. es003-1.jpg es003-2.jpg es004-1.jpg es005-1.jpg es006-1.jpg

Answer 1

Answer:

$a=2q^2r$

$b=3s^2t$

Step-by-step explanation:

We have been given an expression $8q^6r^3+27s^6t^3$ and we are asked to factor our given expression using the identity for the sum of two cubes.

Using exponent property $a^{m*n}=(a^m)^n$ we can write terms of our given expression as:

$q^6=(q^2)^3$

$s^6=(s^2)^3$

We can also write our given numbers as:

$8=2^3$  

$27=3^3$

Upon substituting these values in our given expression we will get,

$(2q^2r)^3+(3s^2t)^3$

Now using sum of cubes identity $a^3+b^3=(a+b)(a^2-ab+b^2)$ we can represent our expression as:

$(2q^2r)^3+(3s^2t)^3=(2q^2r+3s^2t)((2q^2r)^2-(2q^2r*3s^2t)+(3s^2t)^2)$

Upon simplifying we will get,

$(2q^2r)^3+(3s^2t)^3=(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)$

Upon comparing our equation to sum of cubes identity we can see that:

$a=2q^2r$ and $b=3s^2t$

Answer 2

a is 2q^2r

b is 3s^2t

the expression factored is...

(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)