ISEE Upper Level Quantitative Reasoning › How to multiply exponential variables
Multiply:
This can be achieved by using the pattern of difference of squares:
Applying the binomial square pattern:
Simplify:
First, simplify all of the exponents. When the exponent is outside of the parantheses, multiply it by the exponents inside so that you get: . Multiply
so that you get 27. Then, multiply like terms. First, multilpy 2 by 27 so that you get 54. Then, multiply the x terms. Remember, when bases are the same, add the exponents:
. Then, multiply the y terms:
. Then, multiply all of the terms together so that you get
.
Simplify the following:
None of the other answers
To multiply variables with exponents, add the exponents. With multiple variables, simply add the exponents for each different variable.
Simplified:
Factor completely:
The greatest common factor of the terms in is
, so factor that out:
Since all factors here are linear, this is the complete factorization.
Simplify:
Simplify the following:
None of the other answers
To multiply variables with exponents, add the exponents. When there are constants mixed in, multiply the constants separately and put back in the final result:
Fill in the box to form a perfect square trinomial:
To obtain the constant term of a perfect square trinomial, divide the linear coefficient, which here is 20, by 2, and square the quotient. The result is
Simplify the following expression:
Simplify the following expression:
To combine these, we need to multiply our coefficients and our variables.
First, multiply the coefficients
Next, multiply our variables by adding the exponent:
So, we put it all together to get:
Solve the following:
To multiply like variable with exponents, we will use the following formula:
Also, we will multiply coefficients like normal.
So, we get
Multiply the following:
To multiply like variables with exponents, we will use the following formula:
So, we get