Answer :
Sure, I'll provide the detailed, step-by-step solution for finding the product of the given expressions.
We need to find the product of:
[tex]\[ \left(-2x - 9y^2\right)(-4x - 3) \][/tex]
To do this, we'll distribute each term in the first parentheses to each term in the second parentheses.
First, distribute [tex]\(-2x\)[/tex]:
[tex]\[ -2x \cdot -4x = 8x^2 \][/tex]
[tex]\[ -2x \cdot -3 = 6x \][/tex]
Next, distribute [tex]\(-9y^2\)[/tex]:
[tex]\[ -9y^2 \cdot -4x = 36xy^2 \][/tex]
[tex]\[ -9y^2 \cdot -3 = 27y^2 \][/tex]
Now, combine all these terms together:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
Thus, the product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
So the correct choice from the given options is:
[tex]\[ 8 x^2 + 6 x + 36 x y^2 + 27 y^2 \][/tex]
Which corresponds to the option:
[tex]\[ 8 x^2+6 x+36 x y^2+27 y^2 \][/tex]
We need to find the product of:
[tex]\[ \left(-2x - 9y^2\right)(-4x - 3) \][/tex]
To do this, we'll distribute each term in the first parentheses to each term in the second parentheses.
First, distribute [tex]\(-2x\)[/tex]:
[tex]\[ -2x \cdot -4x = 8x^2 \][/tex]
[tex]\[ -2x \cdot -3 = 6x \][/tex]
Next, distribute [tex]\(-9y^2\)[/tex]:
[tex]\[ -9y^2 \cdot -4x = 36xy^2 \][/tex]
[tex]\[ -9y^2 \cdot -3 = 27y^2 \][/tex]
Now, combine all these terms together:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
Thus, the product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
So the correct choice from the given options is:
[tex]\[ 8 x^2 + 6 x + 36 x y^2 + 27 y^2 \][/tex]
Which corresponds to the option:
[tex]\[ 8 x^2+6 x+36 x y^2+27 y^2 \][/tex]
