Class 8 Exam > Class 8 Videos > Multiplying a Monomial with a Binomial
Multiplying a Monomial with a Binomial Video Lecture - Class 8
FAQs on Multiplying a Monomial with a Binomial Video Lecture - Class 8
| 1. What is a monomial and a binomial? |  |
A monomial is an algebraic expression with only one term, such as 3x or 2y^2. A binomial, on the other hand, consists of two terms, such as 4x + 2y or 3a - 7b^2.
| 2. How do you multiply a monomial with a binomial? | |
To multiply a monomial with a binomial, you need to use the distributive property. Distribute the monomial term to each term of the binomial, and then simplify the expression by combining like terms if possible. For example, to multiply 3x by (4x + 2y), you would distribute the 3x to both terms inside the parentheses: 3x * 4x + 3x * 2y = 12x^2 + 6xy.
| 3. Can you provide an example of multiplying a monomial with a binomial? | |
Certainly! Let's consider the monomial 2a multiplied by the binomial (3a + 5b). We distribute the 2a to both terms inside the parentheses: 2a * 3a + 2a * 5b = 6a^2 + 10ab. So, the result of multiplying the monomial 2a with the binomial (3a + 5b) is 6a^2 + 10ab.
| 4. What happens if the binomial has a negative term? | |
If the binomial has a negative term, you still apply the distributive property as usual. Just make sure to distribute the monomial to both terms, including the negative sign. For example, if you want to multiply -2x by (3x - 4y), you would distribute the -2x to both terms: -2x * 3x - 2x * 4y = -6x^2 + 8xy.
| 5. Can you simplify the result after multiplying a monomial with a binomial? | |
Yes, after multiplying a monomial with a binomial, you can simplify the resulting expression by combining like terms if possible. Like terms are those that have the same variables with the same exponents. For example, if you multiply 2x by (3x + 4) to get 6x^2 + 8x, you can simplify it further by combining the x terms: 6x^2 + 8x = 6x^2 + 8x.
Text Transcript from Video
okay so let us continue our discussion
further and see how we can do some more
complex multiplications of expressions
in this video we will explore how do we
multiply a monomial by a binomial so
monomial has one term and a binomial has
two terms so the example that we are
going to look at is multiply 2x by 7y
plus 2x and when you write down the
multiplication it will be 2x x 7 5 plus
2x now the first step to remember is to
simplify and we simplify this expression
over here by using the distributive law
of multiplication and what essentially
we will do is we first multiply this 2x
by 7 by and then the product of these
two terms will be added to the product
of 2 X by 2 X so that is what we are
going to do over here so when we open up
the braces what we get over here is 2x x
7y plus 2x x 2x now as you see what we
have done is we have reduced a monomial
into a binomial multiplication into just
monomial multiplication and then adding
the products okay now if you know how to
multiply a monomial by another monomial
all we do is we just multiply the
coefficients here the 2 times 7 and we
multiply the variables X Y so we have 2
times 7 into x times y plus again same
thing we do or 2 times 2 is this and
then we have x times X which is the
variables over here
okay so when we solve this simplify this
we have 14 times X y plus 4 x squared
right so the step 2 is essentially
monomial multiplication so to summarize
how do we do mono
by a binomial we first use the
distributive law of multiplication and
open up the braces and then what we need
to do is to do two multiplications of
monomial by monomial and then add the
products to get the Sun so that is how
you would do a monomial by a binomial
multiplication
further and see how we can do some more
complex multiplications of expressions
in this video we will explore how do we
multiply a monomial by a binomial so
monomial has one term and a binomial has
two terms so the example that we are
going to look at is multiply 2x by 7y
plus 2x and when you write down the
multiplication it will be 2x x 7 5 plus
2x now the first step to remember is to
simplify and we simplify this expression
over here by using the distributive law
of multiplication and what essentially
we will do is we first multiply this 2x
by 7 by and then the product of these
two terms will be added to the product
of 2 X by 2 X so that is what we are
going to do over here so when we open up
the braces what we get over here is 2x x
7y plus 2x x 2x now as you see what we
have done is we have reduced a monomial
into a binomial multiplication into just
monomial multiplication and then adding
the products okay now if you know how to
multiply a monomial by another monomial
all we do is we just multiply the
coefficients here the 2 times 7 and we
multiply the variables X Y so we have 2
times 7 into x times y plus again same
thing we do or 2 times 2 is this and
then we have x times X which is the
variables over here
okay so when we solve this simplify this
we have 14 times X y plus 4 x squared
right so the step 2 is essentially
monomial multiplication so to summarize
how do we do mono
by a binomial we first use the
distributive law of multiplication and
open up the braces and then what we need
to do is to do two multiplications of
monomial by monomial and then add the
products to get the Sun so that is how
you would do a monomial by a binomial
multiplication
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Nov 23, 2024 Last updated |
Multiplying a Monomial with a Binomial for Class 82024 is part of Class 8 preparation. The notes and questions for Multiplying a Monomial with a Binomial
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