) Factorize fully
1. 2x^2yz-32x^2y^3z

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2x²yz(1 - 4y)(1 + 4y)

Step-by-step explanation:

Given

2x²yz - 32x²y³z ← factor out 2x²yz from each term

= 2x²yz(1 - 16y²) ← difference of squares

= 2x²yz(1 - 4y)(1 + 4y)

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb