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Answer :
To find the product
[tex]$$\left(-2x - 9y^2\right)(-4x - 3),$$[/tex]
we multiply each term in the first parentheses by each term in the second.
1. Multiply the first term of the first polynomial by each term in the second:
- 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]
2. Multiply the second term of the first polynomial by each term in the second:
- 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]
3. Combine all the resulting terms:
[tex]$$8x^2 + 6x + 36xy^2 + 27y^2.$$[/tex]
Thus, the product is:
[tex]$$8x^2 + 6x + 36xy^2 + 27y^2.$$[/tex]
[tex]$$\left(-2x - 9y^2\right)(-4x - 3),$$[/tex]
we multiply each term in the first parentheses by each term in the second.
1. Multiply the first term of the first polynomial by each term in the second:
- 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]
2. Multiply the second term of the first polynomial by each term in the second:
- 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]
3. Combine all the resulting terms:
[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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