10. Simplify 3(2x+5)-{-x+2[2-3(1+x)]}+[-x+2(-x+5)]
11. What is the degree of 7xy^5z^3
12. What is the degree of the polynomial 2a^2be-d^3e^2 f +5g^2h^3i^2
Answer:
10.Distribute the negative sign inside the second set of brackets:
-{-x+2[2-3(1+x)]} = x - 2[2 - 3(1 + x)]
Distribute the negative sign inside the third set of brackets:
[-x+2(-x+5)] = -x - 2x + 10 = -3x + 10
Now, substitute the above results back into the original expression:
3(2x+5) - {-x+2[2-3(1+x)]} + [-x+2(-x+5)]
= 3(2x+5) - (x - 2[2 - 3(1 + x)]) + (-3x + 10)
Distribute the constants:
= 6x + 15 - x + 2(2 - 6x + 3x) - 3x + 10
Simplify within the brackets:
= 6x + 15 - x + 4 - 12x + 6x - 3x + 10
Combine like terms:
= (6x - x - 12x + 6x - 3x) + (15 + 4 + 10)
= -4x + 29
The simplified expression is -4x + 29
11. Degree = Exponent of x + Exponent of y + Exponent of z
Degree = 1 + 5 + 3
Degree = 9
So, the degree of the term 7xy^5z^3 is 9.
12.Term 1: 2a^2be
Degree = 2 (exponent of a) + 1 (exponent of b) + 1 (exponent of e) = 4
Term 2: -d^3e^2f
Degree = 3 (exponent of d) + 2 (exponent of e) + 1 (exponent of f) = 6
Term 3: 5g^2h^3i^2
Degree = 2 (exponent of g) + 3 (exponent of h) + 2 (exponent of i) = 7
Now, we find the highest degree among the terms: 7
Therefore, the degree of the given polynomial 2a^2be - d^3e^2f + 5g^2h^3i^2 is 7.