Question

Rewrite the expression as a product of four linear factors:

a) (x - a)(x - b)(x - c)(x - d)
b) (x + a)(x + b)(x + c)(x + d)
c) (x - a)(x + b)(x - c)(x + d)
d) (x - a)(x - b)(x + c)(x + d)

Answer 1

To rewrite the given expressions as products of four linear factors, we can expand each expression and simplify. The resulting expressions will be in the form of a quadratic equation.

Step-by-step explanation:

To rewrite the expression as a product of four linear factors, we first expand the given expression by multiplying the four factors together:

a) (x - a)(x - b)(x - c)(x - d) = x^4 - (a+b+c+d)x^3 + (ab+ac+ad+bc+bd+cd)x^2 - (abc+abd+acd+bcd)x + abcd

b) (x + a)(x + b)(x + c)(x + d) = x^4 + (a+b+c+d)x^3 + (ab+ac+ad+bc+bd+cd)x^2 + (abc+abd+acd+bcd)x + abcd

c) (x - a)(x + b)(x - c)(x + d) = x^4 + (b-a+c-d)x^3 + (-ab+ac-ad-bc+bd-cd)x^2 + (abc-abd-acd+bcd)x - abcd

d) (x - a)(x - b)(x + c)(x + d) = x^4 + (c-d-a-b)x^3 + (ac+ad-bc-bd)x^2 + (-acd+abd+abc-bcd)x - abcd