(2x-3)(x^2+5x-3)=2x+10x^2-15x+9

*Is this correct.?

this is a different problem...

Here's how this one works out:

......x^2 + 5x - 3
............2x - 3
==================
...... -3x^2 - 15x + 9
2x^3 + 10x^2 - 6x
======================
2x^3 + 7x^2 - 21x + 9

I hope this will help.

To check if the expression is correct, you can simplify both sides of the equation and see if they are equal.

On the left side of the equation, you have the expression (2x-3)(x^2+5x-3). To expand this expression, you can use the distributive property.

(2x-3)(x^2+5x-3) = 2x(x^2+5x-3) - 3(x^2+5x-3)

First, distribute the 2x and -3 to the terms inside the parentheses:

= 2x(x^2) + 2x(5x) + 2x(-3) - 3(x^2) - 3(5x) - 3(-3)
= 2x^3 + 10x^2 - 6x - 3x^2 - 15x + 9

Now, combine like terms:

= 2x^3 + (10x^2 - 3x^2) + (-6x - 15x) + 9
= 2x^3 + 7x^2 - 21x + 9

So, the simplified expression on the left side of the equation is 2x^3 + 7x^2 - 21x + 9.

On the right side of the equation, you have 2x + 10x^2 - 15x + 9. This expression is already simplified.

Now, compare the simplified expressions:

2x^3 + 7x^2 - 21x + 9 = 2x + 10x^2 - 15x + 9

Since both sides of the equation are equal, the expression is correct.