Mathematics: If you see this PLEASE HELP

AStep-by-step explanation:empirical formulas are the simplest form of notation so they provide the lowest whole number ratio between the elements in a compound...

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amunnik04

22.01.2022

Mathematics

Given:

$1. -3 x^{2}\left(4 x^{3}-7\right)\\$2. $(6 x-5)(2 x+3)$\\3. $(3 x-1)\left(x^{2}+5 x-2\right)$$

To find:

The product of the polynomials.

Solution:

1. $-3 x^{2}\left(4 x^{3}-7\right)$ $=-3 x^{2}(4 x^{3}) -3 x^{2}(-7)$

Multiply the numerical coefficient and add the powers of x.

$=-12 x^{5}+21 x^{2}$

2. (6 x-5)(2 x+3)=6 x(2 x+3)-5(2x+3)

Multiply each term of first polynomial with each term of 2nd polynomial.

Multiply the numerical coefficient and add the powers of x.

=12 x^2+18x-10 x-15

=12 x^2+8x-15

3. $(3 x-1)\left(x^{2}+5 x-2\right)=3 x(x^{2}+5 x-2)-1(x^{2}+5 x-2)$

Multiply each term of first polynomial with each term of 2nd polynomial.

Multiply the numerical coefficient and add the powers of x.

$=3x^{3}+15 x^2-6x-x^{2}-5 x+2$

Add or subtract like terms together.

$=3x^{3}+14 x^2-11x+2$

The answer for multiplying polynomials:

$1. -12 x^{5}+21 x^{2}$

$2. \ 12 x^2+8x-15$

$3. \ 3x^{3}+14 x^2-11x+2$

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