Question

Factor out the GCF without simplifying:

(y–6) ^2+(x−1) ^6−6)

A. 2[(y−6) ^2 +(x−1) ^3−3]
B. (y−6) ^2 +(x−1)^3 ]-3 C.3[(y−6) ^2+(x−1) ^6−2]
D. 2[(y−6) ^2 +(x−1) ^6−3]

Answer 1

The factored form without simplifying is
`\(2[(y-6)^2 + (x-1)^6 - 3]\)`.

Thus the correct option is (D).

Step-by-step explanation:

To factor out the greatest common factor (GCF) without simplifying, observe the terms
`\((y-6)^2\)` and
`\((x-1)^6\)`in the given expression
`\( (y-6)^2 + (x-1)^6 - 6 \).` The GCF for these terms is 2 as it is the largest power common to both. Factoring it out gives
`\( 2[(y-6)^2 + (x-1)^6 - 3] \)`, which matches option D.

The factorization process involves identifying the highest power shared by both terms and factoring it out. In this case, the GCF is 2, and the factored expression maintains the structure of the original, ensuring that when the GCF is distributed back, the original expression is recovered.

Therefore, option D,
`\(2[(y-6)^2 + (x-1)^6 - 3]\),` accurately represents the factored form without simplifying for the given expression
`\( (y-6)^2 + (x-1)^6 - 6 \)`. This method of factoring out the GCF is essential for preserving the algebraic structure of the expression while simplifying it.

Thus the correct option is (D).