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Answer :
To solve the product
[tex]$$\left(-2x - 9y^2\right)(-4x - 3),$$[/tex]
we use the distributive property (also known as the FOIL method for binomials). This means multiplying each term in the first parenthesis by each term in the second parenthesis. Here are the steps:
1. Multiply the first term in the first parenthesis by the first term in the second parenthesis:
[tex]$$-2x \cdot (-4x) = 8x^2.$$[/tex]
2. Multiply the first term in the first parenthesis by the second term in the second parenthesis:
[tex]$$-2x \cdot (-3) = 6x.$$[/tex]
3. Multiply the second term in the first parenthesis by the first term in the second parenthesis:
[tex]$$-9y^2 \cdot (-4x) = 36xy^2.$$[/tex]
4. Multiply the second term in the first parenthesis by the second term in the second parenthesis:
[tex]$$-9y^2 \cdot (-3) = 27y^2.$$[/tex]
Now, add all these products together to get the final result:
[tex]$$8x^2 + 6x + 36xy^2 + 27y^2.$$[/tex]
Thus, the product of [tex]$\left(-2x - 9y^2\right)(-4x - 3)$[/tex] is
[tex]$$\boxed{8x^2 + 6x + 36xy^2 + 27y^2}.$$[/tex]
[tex]$$\left(-2x - 9y^2\right)(-4x - 3),$$[/tex]
we use the distributive property (also known as the FOIL method for binomials). This means multiplying each term in the first parenthesis by each term in the second parenthesis. Here are the steps:
1. Multiply the first term in the first parenthesis by the first term in the second parenthesis:
[tex]$$-2x \cdot (-4x) = 8x^2.$$[/tex]
2. Multiply the first term in the first parenthesis by the second term in the second parenthesis:
[tex]$$-2x \cdot (-3) = 6x.$$[/tex]
3. Multiply the second term in the first parenthesis by the first term in the second parenthesis:
[tex]$$-9y^2 \cdot (-4x) = 36xy^2.$$[/tex]
4. Multiply the second term in the first parenthesis by the second term in the second parenthesis:
[tex]$$-9y^2 \cdot (-3) = 27y^2.$$[/tex]
Now, add all these products together to get the final result:
[tex]$$8x^2 + 6x + 36xy^2 + 27y^2.$$[/tex]
Thus, the product of [tex]$\left(-2x - 9y^2\right)(-4x - 3)$[/tex] is
[tex]$$\boxed{8x^2 + 6x + 36xy^2 + 27y^2}.$$[/tex]
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