Solve (c×b×a)²: Finding the Square of a Three-Variable Product

Question

Insert the corresponding expression:

(c×b×a)2= \left(c\times b\times a\right)^2=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:04 In order to open parentheses with a multiplication operation and an outside exponent
00:08 Raise each factor to the power
00:14 We will apply this formula to our exercise
00:25 This is one possible solution
00:26 In multiplication, the order of factors doesn't matter, therefore the expressions are equal
00:34 We can apply this formula to our exercise, and change the order of factors
00:42 This is another possible solution

Step-by-Step Solution


Step 1: The problem provides the expression (c×b×a)2 \left(c \times b \times a\right)^2 and asks us to expand it.
Step 2: We'll use the exponent rule for the power of a product, which states that (xyz)n=xn×yn×zn (xyz)^n = x^n \times y^n \times z^n . Applying this rule to our expression, we get:
(c×b×a)2=c2×b2×a2 \left(c \times b \times a\right)^2 = c^2 \times b^2 \times a^2
Since multiplication is commutative, the order of the factors doesn't affect the product. Therefore, the expression can also be written as:
(c×b×a)2=a2×b2×c2 \left(c \times b \times a\right)^2 = a^2 \times b^2 \times c^2

Therefore, the correct expressions are c2×b2×a2 c^2 \times b^2 \times a^2 and a2×b2×c2 a^2 \times b^2 \times c^2 .

Answer

a'+b' are correct