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Answer :
To multiply the polynomials, we use the distributive property (also known as the FOIL method when there are two binomials). We have:
[tex]$$
(-2x - 9y^2)(-4x - 3).
$$[/tex]
Step 1. Multiply the first term of the first polynomial by each term of the second polynomial:
- Multiply [tex]$-2x$[/tex] by [tex]$-4x$[/tex]:
[tex]$$
(-2x) \cdot (-4x) = 8x^2.
$$[/tex]
- Multiply [tex]$-2x$[/tex] by [tex]$-3$[/tex]:
[tex]$$
(-2x) \cdot (-3) = 6x.
$$[/tex]
Step 2. Multiply the second term of the first polynomial by each term of the second polynomial:
- Multiply [tex]$-9y^2$[/tex] by [tex]$-4x$[/tex]:
[tex]$$
(-9y^2) \cdot (-4x) = 36xy^2.
$$[/tex]
- Multiply [tex]$-9y^2$[/tex] by [tex]$-3$[/tex]:
[tex]$$
(-9y^2) \cdot (-3) = 27y^2.
$$[/tex]
Step 3. Combine all the terms to get the final product:
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
Thus, the product is
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
[tex]$$
(-2x - 9y^2)(-4x - 3).
$$[/tex]
Step 1. Multiply the first term of the first polynomial by each term of the second polynomial:
- Multiply [tex]$-2x$[/tex] by [tex]$-4x$[/tex]:
[tex]$$
(-2x) \cdot (-4x) = 8x^2.
$$[/tex]
- Multiply [tex]$-2x$[/tex] by [tex]$-3$[/tex]:
[tex]$$
(-2x) \cdot (-3) = 6x.
$$[/tex]
Step 2. Multiply the second term of the first polynomial by each term of the second polynomial:
- Multiply [tex]$-9y^2$[/tex] by [tex]$-4x$[/tex]:
[tex]$$
(-9y^2) \cdot (-4x) = 36xy^2.
$$[/tex]
- Multiply [tex]$-9y^2$[/tex] by [tex]$-3$[/tex]:
[tex]$$
(-9y^2) \cdot (-3) = 27y^2.
$$[/tex]
Step 3. Combine all the terms to get the final product:
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
Thus, the product is
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
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