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Answer :
Sure! Let's break down the multiplication step by step:
We want to multiply two expressions: [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex].
1. Distribute [tex]\((-4x)\)[/tex] across the first expression [tex]\((-2x - 9y^2)\)[/tex]:
- Multiply [tex]\(-4x\)[/tex] by [tex]\(-2x\)[/tex]: [tex]\((-4x) \times (-2x) = 8x^2\)[/tex]
- Multiply [tex]\(-4x\)[/tex] by [tex]\(-9y^2\)[/tex]: [tex]\((-4x) \times (-9y^2) = 36xy^2\)[/tex]
2. Distribute [tex]\((-3)\)[/tex] across the first expression [tex]\((-2x - 9y^2)\)[/tex]:
- Multiply [tex]\(-3\)[/tex] by [tex]\(-2x\)[/tex]: [tex]\((-3) \times (-2x) = 6x\)[/tex]
- Multiply [tex]\(-3\)[/tex] by [tex]\(-9y^2\)[/tex]: [tex]\((-3) \times (-9y^2) = 27y^2\)[/tex]
3. Combine all the terms:
- Collect all the results from steps 1 and 2: [tex]\(8x^2 + 36xy^2 + 6x + 27y^2\)[/tex]
The expanded expression, after performing all the multiplications, is:
[tex]\[ 8x^2 + 36xy^2 + 6x + 27y^2 \][/tex]
This matches one of the options provided:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex] is [tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex].
We want to multiply two expressions: [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex].
1. Distribute [tex]\((-4x)\)[/tex] across the first expression [tex]\((-2x - 9y^2)\)[/tex]:
- Multiply [tex]\(-4x\)[/tex] by [tex]\(-2x\)[/tex]: [tex]\((-4x) \times (-2x) = 8x^2\)[/tex]
- Multiply [tex]\(-4x\)[/tex] by [tex]\(-9y^2\)[/tex]: [tex]\((-4x) \times (-9y^2) = 36xy^2\)[/tex]
2. Distribute [tex]\((-3)\)[/tex] across the first expression [tex]\((-2x - 9y^2)\)[/tex]:
- Multiply [tex]\(-3\)[/tex] by [tex]\(-2x\)[/tex]: [tex]\((-3) \times (-2x) = 6x\)[/tex]
- Multiply [tex]\(-3\)[/tex] by [tex]\(-9y^2\)[/tex]: [tex]\((-3) \times (-9y^2) = 27y^2\)[/tex]
3. Combine all the terms:
- Collect all the results from steps 1 and 2: [tex]\(8x^2 + 36xy^2 + 6x + 27y^2\)[/tex]
The expanded expression, after performing all the multiplications, is:
[tex]\[ 8x^2 + 36xy^2 + 6x + 27y^2 \][/tex]
This matches one of the options provided:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex] is [tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex].
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