Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.
(-2x-3)(3-x)
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Step 1
The given expression is,
(-2x-3)(3-x)
We need to multiply the given polynomials using FOIL method.
Using FOIL method,
On multilying the first terms of the polynomials, we get
(-2x)(3)=-6x
On multilying the outer terms of the polynomials, we get
$\left(-2x\right)\left(-x\right)=2{x}^{2}$
On multilying the internal terms of the polynomials, we get
(-3)(3)=-9
On multilying the last terms of the polynomials, we get
(-3)(-x)=3x
Step 2
On combining all the products, we get
$-6x+\left(2{x}^{2}\right)+\left(-9\right)+\left(3x\right)=2{x}^{2}-3x-9$
Therefore, the required product is $2{x}^{2}-3x-9$

Marcus Herman
Multiply the terms of the polynomials in the order First, Outer, Inner and Last.
$\left(-2x-3\right)\left(3-x\right)=-2x\cdot 3+\left(-2x\right)\left(-x\right)+\left(-3\right)3+\left(-3\right)\left(-x\right)$
Use the laws of exponents to multiply the monomials.
$-2x\cdot 3+\left(-2x\right)\left(-x\right)+\left(-3\right)3+\left(-3\right)\left(-x\right)=-6x+2{x}^{1+1}-9+3x$
$=2{x}^{2}-6x+3x-9$
Now, combine the like terms using the distributive property.
$2{x}^{2}-6x+3x-9=2{x}^{2}+\left(-6+3\right)x-9$
$=2{x}^{2}-3x-9$
Therefore, the product is $2{x}^{2}-3x-9$.