Answered

Simplify the following, showing all your working.

1. [tex]\(3a + 2 + 4a - 6\)[/tex]

2. [tex]\(6ab + 3bc - ab + 5bc\)[/tex]

3. [tex]\(2x + 8 - 3x - 7\)[/tex]

4. [tex]\(3xy + 5x - 5yx\)[/tex]

5. [tex]\(11x^2 - 8x + 1 - 7x + 13x^2 - 11\)[/tex]

6. [tex]\(-8m^2 - (-5m^2)\)[/tex]

7. [tex]\(15x \times 3y\)[/tex]

8. [tex]\(x^3 \times x^2 y\)[/tex]

9. [tex]\(2mn^2 \times (-3m^2)\)[/tex]

10. [tex]\(4w^2 y^5 \times 6w^5 y^3\)[/tex]

11. [tex]\(-2(-3a^3b)^2\)[/tex]

12. [tex]\((2x^3y)^2\)[/tex]

13. [tex]\(-5(2x^3y)^2\)[/tex]

14. [tex]\(6x^0\)[/tex]

15. [tex]\((2yx)^0\)[/tex]

16. [tex]\(\frac{18p^2q^5}{-12p^5}\)[/tex]

17. [tex]\(\left(6p^5\right)^2 \div 4p^2\)[/tex]



Answer :

GinnyAnswer
Let's simplify each of the expressions step-by-step:

### Problem 1.1
Simplify the expression [tex]\(3a + 2 + 4a - 6\)[/tex]:
[tex]\[ 3a + 4a + 2 - 6 = 7a - 4 \][/tex]
Answer: [tex]\(7a - 4\)[/tex]

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### Problem 1.2
Simplify the expression [tex]\(26ab + 3bc - ab + 5bc\)[/tex]:
[tex]\[ 26ab - ab + 3bc + 5bc = 25ab + 8bc \][/tex]
Answer: [tex]\(25ab + 8bc\)[/tex]

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### Problem 1.3
Simplify the expression [tex]\(2x + 8 - 3x - 7\)[/tex]:
[tex]\[ 2x - 3x + 8 - 7 = -x + 1 \][/tex]
Answer: [tex]\(-x + 1\)[/tex]

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### Problem 1.4
Simplify the expression [tex]\(43xy + 5x - 5yx\)[/tex]:
Since [tex]\(43xy\)[/tex] and [tex]\(-5yx\)[/tex] are like terms and [tex]\(yx = xy\)[/tex]:
[tex]\[ 43xy - 5xy + 5x = 38xy + 5x \][/tex]
Answer: [tex]\(38xy + 5x\)[/tex]

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### Problem 1.5
Simplify the expression [tex]\(11x^2 - 8x + 1 - 7x + 13x^2 - 11\)[/tex]:
Combine like terms:
[tex]\[ (11x^2 + 13x^2) + (-8x - 7x) + (1 - 11) = 24x^2 - 15x - 10 \][/tex]
Answer: [tex]\(24x^2 - 15x - 10\)[/tex]

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### Problem 1.6
Simplify the expression [tex]\(-8m^2 - (-5m^2)\)[/tex]:
[tex]\[ -8m^2 + 5m^2 = -3m^2 \][/tex]
Answer: [tex]\(-3m^2\)[/tex]

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### Problem 2.1
Simplify the expression [tex]\(15x \times 3y\)[/tex]:
[tex]\[ 15x \cdot 3y = 45xy \][/tex]
Answer: [tex]\(45xy\)[/tex]

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### Problem 2.2
Simplify the expression [tex]\(x^3 \times x^2y\)[/tex]:
[tex]\[ x^3 \cdot x^2 y = x^{3+2} y = x^5y \][/tex]
Answer: [tex]\(x^5y\)[/tex]

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### Problem 2.3
Simplify the expression [tex]\(32mn^2 \times (-3m^2)\)[/tex]:
[tex]\[ 32mn^2 \cdot (-3m^2) = -96m^{1+2} n^2 = -96m^3 n^2 \][/tex]
Answer: [tex]\(-96m^3 n^2\)[/tex]

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### Problem 2.4
Simplify the expression [tex]\(4w^2y^5 \times 6w^5y^3\)[/tex]:
[tex]\[ 4w^2y^5 \cdot 6w^5y^3 = 4 \cdot 6 \cdot w^{2+5} \cdot y^{5+3} = 24w^7y^8 \][/tex]
Answer: [tex]\(24w^7y^8\)[/tex]

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### Problem 2.5
Simplify the expression [tex]\(-2(3a^3b)^2\)[/tex]:
[tex]\[ -2 \cdot (3a^3b)^2 = -2 \cdot 9a^{6}b^{2} = -18a^6b^2 \][/tex]
Answer: [tex]\(-18a^6b^2\)[/tex]

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### Problem 2.6
Simplify the expression [tex]\((2x^3y)^2\)[/tex]:
[tex]\[ (2x^3y)^2 = 4x^{6}y^2 \][/tex]
Answer: [tex]\(4x^6y^2\)[/tex]

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### Problem 2.7
Simplify the expression [tex]\(-5(2x^3y)^2\)[/tex]:
[tex]\[ -5 \cdot (2x^3y)^2 = -5 \cdot 4x^{6}y^2 = -20x^6y^2 \][/tex]
Answer: [tex]\(-20x^6y^2\)[/tex]

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### Problem 2.8
Simplify the expression [tex]\(6x^0\)[/tex]:
Since any number raised to the power of zero is 1:
[tex]\[ 6 \cdot 1 = 6 \][/tex]
Answer: [tex]\(6\)[/tex]

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### Problem 2.9
Simplify the expression [tex]\((2yx)^0\)[/tex]:
Since any expression raised to the power of zero is 1:
[tex]\[ (2yx)^0 = 1 \][/tex]
Answer: [tex]\(1\)[/tex]

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### Problem 2.10
Simplify the expression [tex]\(\frac{18p^2q^5}{-12p^5}\)[/tex]:
[tex]\[ \frac{18p^2q^5}{-12p^5} = \frac{18}{-12} \cdot \frac{p^2}{p^5} \cdot q^5 = -\frac{3}{2} \cdot p^{-3} \cdot q^5 = -\frac{3q^5}{2p^3} \][/tex]
Answer: [tex]\(-\frac{3q^5}{2p^3}\)[/tex]

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### Problem 2.11
Simplify the expression [tex]\(\left (6p^5\right)^2 \div 4p^2\)[/tex]:
[tex]\[ \left (6p^5\right)^2 \div 4p^2 = \frac{36p^{10}}{4p^2} = 9p^{10-2} = 9p^8 \][/tex]
Answer: [tex]\(9p^8\)[/tex]

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