Exercise 31 Page 69

We want to completely factor the given expression. To do so, we will first identify and factor out the greatest common factor (GCF), the common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 3k.

3k^3-24k^2+48k

SplitIntoFactors

Split into factors

3k(k^2)- 3k(8k)+ 3k(16)

FactorOut

Factor out 3k

3k(k^2-8k+16)

Notice that k^2=k^2, 16=4^2 and - 8k=(- 2)* 4* k. Therefore, we can rewrite the given expression as perfect square trinomial. 3k(k^2-8k+16) ⇔ 3k(k-4)^2

Checking Our Answer

Check Our Answer ✓

We can expand our answer and compare it with the given expression.

3k (k-4)^2

ExpandNegPerfectSquare

(a-b)^2=a^2-2ab+b^2

3k(k^2-8k+16)

Distr

Distribute 3k

3k^3-24k^2+48k

We can see above that after expanding and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!