Multiplication of Algebraic Expressions: Rules On Exponents
Multiplication of Algebraic Expressions: Rules On Exponents
Multiplication of Algebraic Expressions: Rules On Exponents
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Multiplication of Algebraic Expressions
Rules on Exponents
Multiplication of algebraic expressions require knowledge of some of the
rules on exponents. These rules are as follows:
Rule #1: Multiplication Rule
xm·xn = xm+n
Ex. x3·x5 = x8
Rule #2: Power of a Power Rule
(xm)n = xmn
Ex. (x3)5 = x15
Rule #3: Power of a Product Rule
(xy)m = xmym
Ex. (xy)5 = x5y5
Course Module
Multiplying a Single Term to an Algebraic Expression with More Than
One Term
To multiply a single term to an algebraic expression with several terms,
distribute the single term to all of the terms of the algebraic expression. Don’t
forget to follow the sign rules when multiplying: The product of expressions
having the same signs is positive while the product of two expression having
different signs is negative. To illustrate, consider multiplying
3x2yz by (4xy5z – 5x3y2z5 + 8x2yz)
We distribute 3x2yz to all of the terms of
(4xy5z – 5x3y2z5 + 8x2yz)…
(3x2yz)(4xy5z) – (3x2yz)(5x3y2z5) + (3x2yz)(8x2yz)
This will give us 12x3y6z2 – 15x5y3z6 + 24x4y2z2.
Let us try another one.
(–4a3b2c)(3a2bc4 – 7abc9 + 8a5c)
= – (4a3b2c)(3a2bc4) + (4a3b2c)(7abc9) – (4a3b2c)(8a5c)
The signs are already adjusted following the sign rules of multiplication.
The final answer would be
–12a5b3c5 + 28a4b3c10 – 32a8b2c2
First-Outer-Inner-Last
We demonstrate this by multiplying the expressions (3x2 – 4yz3) and (5x3y –
6xz2).
First – means we multiply the first terms: 3x2 and 5x3y
2. Multiply the first term of the first row by the terms of the second row.
Write the products on the row below them.
3x + 5y
4x – 7y
12x2 – 21xy
3. Multiply the second term of the first row by the terms of the second row.
Write the products on the row below the products from the previous step.
We have to see to it that we align similar terms (in this case, – 21xy and
20xy)
3x + 5y
4x – 7y
12x2 – 21xy
20xy – 35y2
4. Combine similar terms to get the final answer
3x + 5y
4x – 7y
12x2 – 21xy
Course Module
20xy – 35y2
12x2 – xy – 35y2
We can also use this process to multiply algebraic expressions composed of
three or more terms.
8x + 7y – 4z
2x – 4y + 5z
16x2 – 32xy + 40xz
3. Multiply the second term of the first row by the terms of the second row.
Write the products on the row below the products from the previous step.
We have to see to it that we align similar terms (in this case, – 32xy and
14xy)
8x + 7y – 4z
2x – 4y + 5z
16x2 – 32xy + 40xz
14xy – 28y2 + 35yz
4. Multiply the last term of the first row by the terms of the second row.
8x + 7y – 4z
2x – 4y + 5z
16x2 – 32xy + 40xz
14xy – 28y2 + 35yz
– 8xz + 16yz – 20z2
5. Combine similar terms to get the final answer.
8x + 7y – 4z
2x – 4y + 5z
16x2 – 32xy + 40xz
College Algebra
5
Multiplication of Algebraic Expressions
References
Vance, E.P. (1984). Modern Algebra and Trigonometry, 3rd Ed. Addison
Wesley
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