Which polynomial represents the sum below?
1 answer:
The correct answer is: [D]: " 4x² − 12x − 4 " .___________________________________________________ Explanation: ___________________________________________________ Given: ___________________________________________________ " (16x² − 16) + ( -12x² − 12x + 12) " ; Simplify.___________________________________________________ Note the "distributive property of multiplication: ___________________________________________________ a(b + c) = ab + ac ; a(b − c) = ab − ac . ___________________________________________________ So we can rewrite the expression as: " (16x² − 16) + 1( -12x² − 12x + 12) " ; {The "1" is implied; since "1", multiplied by any value, results in the exact same value.}. Let us examine the following part of the expression:_________________________________________________ " + 1 ( -12x² − 12x + 12 ) " ; Using the distributive property of multiplication: " + 1 ( -12x² − 12x + 12 ) = (1 * -12x²) − (1 * 12x) + (1 * 12) ; = " − 12x² − 12x + 12 " ; _________________________________________________ Now, bring down the other part of the expression; & rewrite:_________________________________________________ → " (16x² − 16) − 12x² − 12x + 12 " ; → " 16x² − 16 − 12x² − 12x + 12 " ; Now, combine the "like terms" : + 16x² − 12x² = 4x² ; − 16 + 12 = -4 ; and we have " − 12x" ; So we can rewrite the expression as:_______________________________________________________ → " 4x² − 12x − 4 " ; → which is: "Answer choice: [D]: " 4x² − 12x − 4 <span>" . </span>_______________________________________________________
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