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Introduction on Multiplication of Algebraic Expression
Multiplication of algebraic expressions is the process of multiplying two or more algebraic expressions together. The result of the multiplication is another algebraic expression.
To multiply two algebraic expressions together, you simply multiply the coefficients of the expressions together and then multiply the variables together. For example, if you wanted to multiply 3x2y3 and 5x2y, you would first multiply 3 and 5 together to get 15. Then, you would multiply 2 and 3 together to get 6. Finally, you would multiply x and y together to get 6. So, the final answer would be 15x6y.
What are the Algebraic expressions in maths?
An algebraic expression is a mathematical formula that uses letters to represent numbers. For example, the algebraic expression 3x + 5 represents the sum of 3 multiplied by x and 5.
Algebraic Terms
An algebraic term is a mathematical expression that contains at least one variable. Algebraic terms can be combined to form more complex expressions, and they can be manipulated to solve mathematical problems. Some common algebraic terms include constants, variables, coefficients, and powers.
Polynomial Expression
A polynomial expression is an algebraic expression that is composed of one or more terms, each of which is a polynomial. A term is a monomial, binomial, or trinomial.
Multiplying Algebraic Expressions:
The product of two algebraic expressions is obtained by multiplying the coefficients of like terms and then adding the products of the variables.
For example, the product of 3x and 2y is 6x2y.
Multiplication of Monomial by Monomial :
Multiplication of Monomial by Monomial is the process of multiplying two monomials together. The result is a new monomial.
To multiply two monomials together, simply multiply the coefficients of like terms and add the terms together.
For example, to multiply 3x2y3 by 5×4, multiply the coefficients (3×2)(5×4) = 15×8 and add the terms (3x2y3)(5×4) = 15x8y3.
Multiplying Monomials and Polynomials:
Multiplying monomials is easy. Just multiply the coefficients and add the products of the variables.
For example, if you have 3x and 5y, the product is 15x+25y.
Multiplying polynomials is a little more complicated. You have to use the distributive property and then combine like terms.
For example, if you have 3x^2+5x-4 and 2x^3-7x^2+3x, the product is 6x^3-2x^2+8x-7.
Multiplication of Two Binomials
To multiply two binomials, use the distributive property to multiply each term of the first binomial by each term of the second binomial.
For example, to multiply (x + y) by (x − y), use the distributive property to multiply each term of the first binomial by each term of the second binomial.
(x + y) (x − y)
= x(x − y) + y(x − y)
