Question

Given the expression: 4x10 − 64x2

Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)

Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Answer 1

Part A

4x10 – 64x2

= 4x2 * x8 – 4x2 * 16

= 4x2 * (x8 – 16) by distributive property

Part B

x8 is (x4)2 and 16 = 42 so a difference of squares is seen in the parentheses. The pattern a2 – b2 = (a + b)(a – b) can be used.

4x2 * (x8 – 16)

= 4x2 * (x4 + 4) * (x4 – 4)

x4 = (x2)2 and 4 = 22 so there is another difference of squares in the last factor. Use the pattern again.

= 4x2 * (x4 + 4) * (x2 + 2) * (x2 – 2)

here's your answer .

Answer 2

Answer:

Step-by-step explanation:

Part A: What is the greatest common factor? Explain how to find it. (3 points)

Part B: Factor the expression completely. Show all necessary steps. (5 points)

Part C: Check your factoring from Part B by multiplying. Show all necessary steps. (2 points)