(x + 3)(x^2 – 2x + 7)

=x(x^2 – 2x + 7) +3(x^2 – 2x + 7)

distributive property

x(x^2 – 2x + 7)+3(x^2 – 2x + 7)

= x^3-2x^2+7x + 3x^2-6x+21
= x^3-2x^2+3x^2+7x-6x+21
= x^3+x^2+x+21 ---- this is the answer

To multiply the expression (x + 3)(x^2 - 2x + 7), we need to use the distributive property.

Step 1: Multiply the first term of the first binomial, x, with each term of the second trinomial, x^2 - 2x + 7:
(x)(x^2 - 2x + 7) = x^3 - 2x^2 + 7x

Step 2: Multiply the second term of the first binomial, 3, with each term of the second trinomial:
(3)(x^2 - 2x + 7) = 3x^2 - 6x + 21

Step 3: Combine the results from Step 1 and Step 2:
(x^3 - 2x^2 + 7x) + (3x^2 - 6x + 21) = x^3 + (-2x^2 + 3x^2) + (7x - 6x) + 21

Step 4: Simplify the expression by combining like terms:
x^3 + (1x^2) + (x) + 21 = x^3 + x^2 + x + 21

So, (x + 3)(x^2 - 2x + 7) simplifies to x^3 + x^2 + x + 21.