Vanessa uses the expressions open paren 3 x squared plus 5 x plus 10 close paren and open paren x squared minus 3 x minus 1 close paren to represent the length and width of her patio. Which expression represents the area l w of Vanessa’s patio?
Answer
A
3 x to the 4th power plus 14 x cubed plus 28 x squared plus 35 x plus 10
B
3 x to the 4th power minus 4 x cubed plus 22 x squared plus 35 x plus 10
C
3 x to the 4th power minus 4 x cubed minus 8 x squared minus 35 x minus 10
Explanation
Multiply each term in the length by each term in the width, then combine like terms: 3x²·(x² − 3x − 1) + 5x·(x² − 3x − 1) + 10·(x² − 3x − 1) = 3x⁴ − 4x³ − 8x² − 35x − 10. This matches choice C, 3x⁴ − 4x³ − 8x² − 35x − 10.
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