Whether you're a student or a professional, IDNLearn.com has answers for everyone. Find reliable solutions to your questions quickly and easily with help from our experienced experts.
Sagot :
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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### Problem 2.1
Simplify the expression [tex]\(15x \times 3y\)[/tex]:
[tex]\[ 15x \cdot 3y = 45xy \][/tex]
Answer: [tex]\(45xy\)[/tex]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### Problem 2.1
Simplify the expression [tex]\(15x \times 3y\)[/tex]:
[tex]\[ 15x \cdot 3y = 45xy \][/tex]
Answer: [tex]\(45xy\)[/tex]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
### 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]
---
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.
