Question

(7x+1)(-7x)(2x-3)

Answer 1

To simplify the expression \((7x + 1)(-7x)(2x - 3)\), we can follow these steps:

1. First, simplify the product of the first two factors, \((7x + 1)(-7x)\):
\[
(7x + 1)(-7x) = -7x(7x) - 7x(1) = -49x^2 - 7x
\]

2. Next, we will multiply this result by the third factor \((2x - 3)\):
\[
(-49x^2 - 7x)(2x - 3)
\]

We will use the distributive property to multiply each term in \(-49x^2 - 7x\) by each term in \(2x - 3\):

- First, multiplying \(-49x^2\) by \(2x\):
\[
-49x^2 \cdot 2x = -98x^3
\]

- Next, multiplying \(-49x^2\) by \(-3\):
\[
-49x^2 \cdot -3 = 147x^2
\]

- Now, multiplying \(-7x\) by \(2x\):
\[
-7x \cdot 2x = -14x^2
\]

- Finally, multiplying \(-7x\) by \(-3\):
\[
-7x \cdot -3 = 21x
\]

3. Now we combine all the products:
\[
-98x^3 + 147x^2 - 14x^2 + 21x
\]

4. Combine like terms:
\[
-98x^3 + (147x^2 - 14x^2) + 21x = -98x^3 + 133x^2 + 21x
\]

Thus, the simplified expression is:
\[
\boxed{-98x^3 + 133x^2 + 21x}
\]