Which expression is equivalent to 9 x to the 5th power plus 3 x open paren 4 x to the 4th power minus 3 x squared close paren squared ?
Answer
A
48 x to the 9th power plus 9 x to the 5th power minus 9 x to the 4th power
B
48 x to the 9th power minus 72 x to the 7th power plus 36 x to the 5th power
C
48 x to the 9th power plus 36 x to the 5th power
D
48 x to the 9th power minus 24 x to the 6th power plus 9 x to the 5th power plus 9 x to the 4th power
Explanation
First square the binomial: (4x⁴ − 3x²)² = 16x⁸ − 24x⁶ + 9x⁴. Multiplying by 3x gives 48x⁹ − 72x⁷ + 27x⁵; then add the 9x⁵ outside the parentheses to get 48x⁹ − 72x⁷ + 36x⁵. This is choice B.
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