Question

Please solve this, What is the product of the binomials below?
(d−1)(d+2)(d+3)

Answer 1

d^3-2d^2-5d+6

Explanation:

Step 1: (d-1)(d+2)=d^2+d-2

Step 2: (d-3)(d^2+d-2) = d^3+d^2-2d-3d^2-3d+6 = d^3-2d^2-5d+6

Answer 2

Answer: The product of the binomials (d-1)(d+2)(d+3) is
`d^3 + 4d^2 +d - 6`.

Explanation:

When multiplying the binomials, you can break it down and multiply two expressions first then multiply that last expression:

(d−1)(d+2)(d+3)

first: (d−1)(d+2)

when multiplying expressions you can multiply using the 'box method' where you would draw a box and put each part of the expression on the top and the left side of the box, multiplying each on into the box and adding like terms.

You can also multiply it by first taking the expression, (d−1)(d+2) and multiplying the variable 'd' to the (d + 2) and then multiplying the '-1' to the (d+2) and then adding like terms:

(d−1)(d+2)

`d^(2) + 2d - d - 2`

'd' is the only like term in this expression so lets add 2d and -d together

`d^(2) + d - 2`

finally, we need to multiply the (d + 3) to expression,
`d^(2) + d - 2`

We will treat this multiplying process the same as before.

`(d + 3)(d^(2) + d - 2)`

`d^3 + d^2 -2d + 3d^2 + 3d - 6`

now lets add like terms

`d^3 + 4d^2 +d - 6`

So the product of the binomials (d-1)(d+2)(d+3) is
`d^3 + 4d^2 +d - 6`.