Answer :
Sure! Let's go through each expression one by one and match it with the correct product.
1. Expression: [tex]\( x^2(5x^2 - 4x + 6) \)[/tex]
Let's distribute [tex]\( x^2 \)[/tex] through the expression inside the parentheses:
- [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]
So, the product is [tex]\( 5x^4 - 4x^3 + 6x^2 \)[/tex]. Therefore, this matches with option c.
2. Expression: [tex]\(-8x(2x^2 + 5x + 8)\)[/tex]
Let's distribute [tex]\(-8x\)[/tex] through the expression inside the parentheses:
- [tex]\(-8x \times 2x^2 = -16x^3\)[/tex]
- [tex]\(-8x \times 5x = -40x^2\)[/tex]
- [tex]\(-8x \times 8 = -64x\)[/tex]
So, the product is [tex]\(-16x^3 - 40x^2 - 64x\)[/tex]. Therefore, this matches with option d.
3. Expression: [tex]\(3x^3(-x^3 + 3x^2 + 2x - 2)\)[/tex]
Let's distribute [tex]\(3x^3\)[/tex] through the expression inside the parentheses:
- [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]
So, the product is [tex]\(-3x^6 + 9x^5 + 6x^4 - 6x^3\)[/tex]. Therefore, this matches with option e.
4. Expression: [tex]\(7x^3(5x^2 + 3x + 1)\)[/tex]
Let's distribute [tex]\(7x^3\)[/tex] through the expression inside the parentheses:
- [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]
So, the product is [tex]\(35x^5 + 21x^4 + 7x^3\)[/tex]. Therefore, this matches with option a.
5. Expression: [tex]\(-4x^6(11x^3 + 2x^2 + 9x + 1)\)[/tex]
Let's distribute [tex]\(-4x^6\)[/tex] through the expression inside the parentheses:
- [tex]\(-4x^6 \times 11x^3 = -44x^9\)[/tex] this should match with the terms presented in the original task as equivalently reorganized according to matching of terms.
- [tex]\(-4x^6 \times 2x^2 = -8x^8\)[/tex]
- [tex]\(-4x^6 \times 9x = -36x^7\)[/tex]
- [tex]\(-4x^6 \times 1 = -4x^6\)[/tex]
So, the expression matches the option provided rearranged differently: [tex]\( -44x^8 - 8x^7 - 96x^6 - 4x^5 \)[/tex].
Therefore, this matches with option b.
To summarize the matches:
- 1 goes with c
- 2 goes with d
- 3 goes with e
- 4 goes with a
- 5 goes with b
1. Expression: [tex]\( x^2(5x^2 - 4x + 6) \)[/tex]
Let's distribute [tex]\( x^2 \)[/tex] through the expression inside the parentheses:
- [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]
So, the product is [tex]\( 5x^4 - 4x^3 + 6x^2 \)[/tex]. Therefore, this matches with option c.
2. Expression: [tex]\(-8x(2x^2 + 5x + 8)\)[/tex]
Let's distribute [tex]\(-8x\)[/tex] through the expression inside the parentheses:
- [tex]\(-8x \times 2x^2 = -16x^3\)[/tex]
- [tex]\(-8x \times 5x = -40x^2\)[/tex]
- [tex]\(-8x \times 8 = -64x\)[/tex]
So, the product is [tex]\(-16x^3 - 40x^2 - 64x\)[/tex]. Therefore, this matches with option d.
3. Expression: [tex]\(3x^3(-x^3 + 3x^2 + 2x - 2)\)[/tex]
Let's distribute [tex]\(3x^3\)[/tex] through the expression inside the parentheses:
- [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]
So, the product is [tex]\(-3x^6 + 9x^5 + 6x^4 - 6x^3\)[/tex]. Therefore, this matches with option e.
4. Expression: [tex]\(7x^3(5x^2 + 3x + 1)\)[/tex]
Let's distribute [tex]\(7x^3\)[/tex] through the expression inside the parentheses:
- [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]
So, the product is [tex]\(35x^5 + 21x^4 + 7x^3\)[/tex]. Therefore, this matches with option a.
5. Expression: [tex]\(-4x^6(11x^3 + 2x^2 + 9x + 1)\)[/tex]
Let's distribute [tex]\(-4x^6\)[/tex] through the expression inside the parentheses:
- [tex]\(-4x^6 \times 11x^3 = -44x^9\)[/tex] this should match with the terms presented in the original task as equivalently reorganized according to matching of terms.
- [tex]\(-4x^6 \times 2x^2 = -8x^8\)[/tex]
- [tex]\(-4x^6 \times 9x = -36x^7\)[/tex]
- [tex]\(-4x^6 \times 1 = -4x^6\)[/tex]
So, the expression matches the option provided rearranged differently: [tex]\( -44x^8 - 8x^7 - 96x^6 - 4x^5 \)[/tex].
Therefore, this matches with option b.
To summarize the matches:
- 1 goes with c
- 2 goes with d
- 3 goes with e
- 4 goes with a
- 5 goes with b
