Answer :
To find the product [tex]\(( -2x - 9y^2)(-4x - 3)\)[/tex], we will use the distributive property to multiply each term in the first expression by each term in the second expression. Let's break it down step by step:
1. Multiply [tex]\((-2x)\)[/tex] by each term in [tex]\((-4x - 3)\)[/tex]:
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex] (Multiplying the coefficients [tex]\(-2\)[/tex] and [tex]\(-4\)[/tex] gives [tex]\(8\)[/tex] and [tex]\(x \times x = x^2\)[/tex])
- [tex]\((-2x) \times (-3) = 6x\)[/tex] (Multiplying the coefficients [tex]\(-2\)[/tex] and [tex]\(-3\)[/tex] gives [tex]\(6\)[/tex])
2. Multiply [tex]\((-9y^2)\)[/tex] by each term in [tex]\((-4x - 3)\)[/tex]:
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex] (Multiplying the coefficients [tex]\(-9\)[/tex] and [tex]\(-4\)[/tex] gives [tex]\(36\)[/tex] and [tex]\(y^2 \times x = xy^2\)[/tex])
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex] (Multiplying the coefficients [tex]\(-9\)[/tex] and [tex]\(-3\)[/tex] gives [tex]\(27\)[/tex])
3. Add all the terms together:
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
The simplified expression of the product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
So, the correct answer is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
1. Multiply [tex]\((-2x)\)[/tex] by each term in [tex]\((-4x - 3)\)[/tex]:
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex] (Multiplying the coefficients [tex]\(-2\)[/tex] and [tex]\(-4\)[/tex] gives [tex]\(8\)[/tex] and [tex]\(x \times x = x^2\)[/tex])
- [tex]\((-2x) \times (-3) = 6x\)[/tex] (Multiplying the coefficients [tex]\(-2\)[/tex] and [tex]\(-3\)[/tex] gives [tex]\(6\)[/tex])
2. Multiply [tex]\((-9y^2)\)[/tex] by each term in [tex]\((-4x - 3)\)[/tex]:
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex] (Multiplying the coefficients [tex]\(-9\)[/tex] and [tex]\(-4\)[/tex] gives [tex]\(36\)[/tex] and [tex]\(y^2 \times x = xy^2\)[/tex])
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex] (Multiplying the coefficients [tex]\(-9\)[/tex] and [tex]\(-3\)[/tex] gives [tex]\(27\)[/tex])
3. Add all the terms together:
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
The simplified expression of the product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
So, the correct answer is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
