Answer:
x³ +7x² +7x -15
Step-by-step explanation:
Apply the distributive property repeatedly, and/or recognize the ways that the coefficients of the product are formed.
distributive property
(x -1)(x +3)(x +5)
= (x -1)(x(x +5) +3(x +5))
= (x -1)(x² +5x +3x +15) = (x -1)(x² +8x +15)
= x(x² +8x +15) -1(x² +8x +15)
= x³ +8x² +15x -x² -8x -15
= x³ +7x² +7x -15
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using knowledge of products of powers
The x³ term will be the product of all of the x-terms.
The x² term will be the pairwise sum of products of two x-terms and the third constant.
The x term will be the pairwise sum of products of one x-term and the two other constants.
The constant term will be the product of all of the constants.
These computations are simplified a bit because all of the x-coefficients are 1.
= x³ +(-1 +3 +5)x² +(-1·3 +(-1)·5 +3·5)x +(-1)·3·5
= x³ +7x² +7x -15
