Simplify the expressions.
1. (-6c^2)(2c^2-3c)
2. (-5d-10d^2)(-6d^3)
3. x^3-(4x+3x^2)(x^2)
4. (-8y^2)(3y-4)+6y^2-5y^3
5. (18m/-4n) / (-1/4m)
6. (5x^2) / (2x/15)
7. (-16x+9) / (-4)
8. (-32-4x) / (-8)
I don't get how to do these. Please help!! Thanks a lot!! =)
First you have to study the laws of exponents, which include:
ax * ay = ax+y
ax / ay = ax-y
ax * ay = (ax+y)y = axy
a-x = 1/ax
a1/x = xth root of a
When you have a multiplication of powers, you would group together factors with the same base and apply the above rules.
I will do the first one to give you a kick-start.
(-6c^2)(2c^2-3c)
= -6 (c²)(2c²-3c)
= -6 (2c2+2 - 3c2+1)
= -6(2c⁴-3c³)
= -12c⁴+18c³)
You can now attempt the rest of the problems and send in your answers for checking if you wish.
Sure! I'll explain how to simplify each expression step by step:
1. (-6c^2)(2c^2-3c)
To simplify this expression, we can use the distributive property. Multiply -6c^2 by each term inside the parentheses:
(-6c^2)*(2c^2) = -12c^4
(-6c^2)*(-3c) = 18c^3
Combine the like terms to get the final simplified expression:
-12c^4 + 18c^3
2. (-5d-10d^2)(-6d^3)
Again, we can use the distributive property here. Multiply -5d by each term inside the parentheses:
(-5d)*(-6d^3) = 30d^4
(-5d)*(-10d^2) = 50d^3
Combine the expressions to get the simplified result:
30d^4 + 50d^3
3. x^3-(4x+3x^2)(x^2)
This expression involves multiplication and subtraction. Use the distributive property to simplify the expression:
-1 * (4x * x^2 + 4x * (-4x) + 3x^2 * x^2)
= -1 * (4x^3 - 16x^2 + 3x^4)
= -4x^3 + 16x^2 - 3x^4
4. (-8y^2)(3y-4)+6y^2-5y^3
Once again, we use the distributive property:
(-8y^2)*(3y) = -24y^3
(-8y^2)*(-4) = 32y^2
Combine the like terms:
-24y^3 + 32y^2 + 6y^2 - 5y^3
= -29y^3 + 38y^2
5. (18m/-4n) / (-1/4m)
To simplify this division expression, remember that dividing by a fraction is the same as multiplying by its reciprocal. In this case:
18m / -4n = (-4n/1) * (18m/-4n)
= -4m
Now, let's divide by -1/4m:
-4m * (4m/-1)
= -4m * (-4m)
= 16m^2
6. (5x^2) / (2x/15)
Here, we have a division of two fractions. To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
(5x^2) / (2x/15) = (5x^2) * (15/2x)
= (5 * 15 * x^2) / (2 * x)
= (75x^2) / (2x)
= 37.5x
7. (-16x+9) / (-4)
Simply divide -16x by -4 and 9 by -4 to get:
(-16x / -4) + (9 / -4)
= 4x - (9/4)
= 4x - 2.25
8. (-32-4x) / (-8)
Divide each term by -8:
-32 / -8 = 4
-4x / -8 = 0.5x
Combine the terms:
4 + 0.5x
or
0.5x + 4
I hope this helps! If you have any further questions, feel free to ask.