Answer :
To match each expression with the correct product, let's distribute each expression step by step:
1. Expression 1: [tex]\(-8x(2x^2 + 5x + 8)\)[/tex]
- Distribute [tex]\(-8x\)[/tex] to each term:
- [tex]\(-8x \times 2x^2 = -16x^3\)[/tex]
- [tex]\(-8x \times 5x = -40x^2\)[/tex]
- [tex]\(-8x \times 8 = -64x\)[/tex]
The product is: [tex]\(-16x^3 - 40x^2 - 64x\)[/tex]
This matches with option d.
2. Expression 2: [tex]\(x^2(5x^2 - 4x + 6)\)[/tex]
- Distribute [tex]\(x^2\)[/tex] to each term:
- [tex]\(x^2 \times 5x^2 = 5x^4\)[/tex]
- [tex]\(x^2 \times -4x = -4x^3\)[/tex]
- [tex]\(x^2 \times 6 = 6x^2\)[/tex]
The product is: [tex]\(5x^4 - 4x^3 + 6x^2\)[/tex]
This matches with option c.
3. Expression 3: [tex]\(7x^3(5x^2 + 3x + 1)\)[/tex]
- Distribute [tex]\(7x^3\)[/tex] to each term:
- [tex]\(7x^3 \times 5x^2 = 35x^5\)[/tex]
- [tex]\(7x^3 \times 3x = 21x^4\)[/tex]
- [tex]\(7x^3 \times 1 = 7x^3\)[/tex]
The product is: [tex]\(35x^5 + 21x^4 + 7x^3\)[/tex]
This matches with option a.
4. Expression 4: [tex]\(3x^3(-x^3 + 3x^2 + 2x - 2)\)[/tex]
- Distribute [tex]\(3x^3\)[/tex] to each term:
- [tex]\(3x^3 \times -x^3 = -3x^6\)[/tex]
- [tex]\(3x^3 \times 3x^2 = 9x^5\)[/tex]
- [tex]\(3x^3 \times 2x = 6x^4\)[/tex]
- [tex]\(3x^3 \times -2 = -6x^3\)[/tex]
The product is: [tex]\(-3x^6 + 9x^5 + 6x^4 - 6x^3\)[/tex]
This matches with option e.
5. Expression 5: [tex]\(-4x^5(11x^3 + 2x^2 + 9x + 1)\)[/tex]
- Distribute [tex]\(-4x^5\)[/tex] to each term:
- [tex]\(-4x^5 \times 11x^3 = -44x^8\)[/tex]
- [tex]\(-4x^5 \times 2x^2 = -8x^7\)[/tex]
- [tex]\(-4x^5 \times 9x = -36x^6\)[/tex]
- [tex]\(-4x^5 \times 1 = -4x^5\)[/tex]
The product is: [tex]\(-44x^8 - 8x^7 - 36x^6 - 4x^5\)[/tex]
This matches with option b.
In summary, the correct matches are:
- 1: d
- 2: c
- 3: a
- 4: e
- 5: b
1. Expression 1: [tex]\(-8x(2x^2 + 5x + 8)\)[/tex]
- Distribute [tex]\(-8x\)[/tex] to each term:
- [tex]\(-8x \times 2x^2 = -16x^3\)[/tex]
- [tex]\(-8x \times 5x = -40x^2\)[/tex]
- [tex]\(-8x \times 8 = -64x\)[/tex]
The product is: [tex]\(-16x^3 - 40x^2 - 64x\)[/tex]
This matches with option d.
2. Expression 2: [tex]\(x^2(5x^2 - 4x + 6)\)[/tex]
- Distribute [tex]\(x^2\)[/tex] to each term:
- [tex]\(x^2 \times 5x^2 = 5x^4\)[/tex]
- [tex]\(x^2 \times -4x = -4x^3\)[/tex]
- [tex]\(x^2 \times 6 = 6x^2\)[/tex]
The product is: [tex]\(5x^4 - 4x^3 + 6x^2\)[/tex]
This matches with option c.
3. Expression 3: [tex]\(7x^3(5x^2 + 3x + 1)\)[/tex]
- Distribute [tex]\(7x^3\)[/tex] to each term:
- [tex]\(7x^3 \times 5x^2 = 35x^5\)[/tex]
- [tex]\(7x^3 \times 3x = 21x^4\)[/tex]
- [tex]\(7x^3 \times 1 = 7x^3\)[/tex]
The product is: [tex]\(35x^5 + 21x^4 + 7x^3\)[/tex]
This matches with option a.
4. Expression 4: [tex]\(3x^3(-x^3 + 3x^2 + 2x - 2)\)[/tex]
- Distribute [tex]\(3x^3\)[/tex] to each term:
- [tex]\(3x^3 \times -x^3 = -3x^6\)[/tex]
- [tex]\(3x^3 \times 3x^2 = 9x^5\)[/tex]
- [tex]\(3x^3 \times 2x = 6x^4\)[/tex]
- [tex]\(3x^3 \times -2 = -6x^3\)[/tex]
The product is: [tex]\(-3x^6 + 9x^5 + 6x^4 - 6x^3\)[/tex]
This matches with option e.
5. Expression 5: [tex]\(-4x^5(11x^3 + 2x^2 + 9x + 1)\)[/tex]
- Distribute [tex]\(-4x^5\)[/tex] to each term:
- [tex]\(-4x^5 \times 11x^3 = -44x^8\)[/tex]
- [tex]\(-4x^5 \times 2x^2 = -8x^7\)[/tex]
- [tex]\(-4x^5 \times 9x = -36x^6\)[/tex]
- [tex]\(-4x^5 \times 1 = -4x^5\)[/tex]
The product is: [tex]\(-44x^8 - 8x^7 - 36x^6 - 4x^5\)[/tex]
This matches with option b.
In summary, the correct matches are:
- 1: d
- 2: c
- 3: a
- 4: e
- 5: b
