(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: $$\boxed{{\displaystyle -98x^3+133x^2+21x}}$$