Students who wish to learn in-depth about the 9th-grade expansion of powers of binomials and trinomials are suggested to make use of our page. Here we have covered all the topics related to the binomial and trinomial expansions with theorems, formulas, examples, and so on. Thus the students who wanna become masters in maths can refer to this page and score top in the exams.
Binomial and trinomial expansions are very important for mathematical study regarding probability theory and approximation techniques. Here the students of 9th grade can learn how to find the specific term or specific power of x. Click on the below-attached links in which you are lagging and prepare as you wish.
Expansion of Powers of Binomials and Trinomials
The topics covered in this chapter are as follows,
- Expansion of (a ± b)^2
- Expansion of (a ± b ± c)^2
- Expansion of (x ± a)(x ± b)
- Express a^2 + b^2 + c^2 – ab – bc – ca as Sum of Squares
- Completing a Square
- Simplification of (a + b)(a – b)
- Application Problems on Expansion of Powers of Binomials and Trinomials
- Worksheet on Expansion of (a ± b)^2 and its Corollaries
- Worksheet on Expanding of (a ± b ± c)^2 and its Corollaries
- Worksheet on Expansion of (x ± a)(x ± b)
- Worksheet on Completing Square
- Worksheet on Simplification of (a + b)(a – b)
- Worksheet on Application Problems on Expansion of Powers of Binomials and Trinomials
- Expansion of (a ± b)^3
- Simplification of (a ± b)(a^2 ∓ ab + b^2)
- Simplification of (a + b + c)(a^2 + b^2 + c^2 – ab – bc – ca)
- Expansion of (x + a)(x + b)(x + c)
- Problems on Expanding of (a ± b)^3 and its Corollaries
An algebraic expression with two terms is known as binomial expression. It contains two different terms a and b or x and y. Here you can learn the details of binomial theorem such as definition, properties, applications, etc.
General terms used in the binomial expansion are general term, middle term, independent term, the ratio of coefficients, numerically greatest term. The binomial theorem is the method of expanding an expression that is to be raised to any determinate power.
(x + y)^n = nΣr=0 nCr x^(n – r) · y^r
In maths, the trinomial expansion is the power of the sum of three terms into the monomials. Here you can learn the properties, formulas, examples from here. The formula of a trinomial is a special case for, m = 3. The coefficients of the terms are written in pascal’s pyramid form.
Expansion of (a ± b)²
A binomial expression is an algebraic expression that has two terms like a and b. The example of a binomial expression is a ± b. (a – b)² and (a + b)² is used to find the square of binomial. Let us discuss the expansion and properties of (a ± b)² from our page.
Expansion of (a ± b ± c)²
A trinomial expression has three terms such as a, b, c. An example of trinomial expansion is (a + b + c)² and (a – b – c)². The trinomial expansion is used to find the square of the trinomial. We will know about the expansion of (a ± b ± c)² and the properties of trinomial expressions from here.
Expansion of (x ± a)(x ± b)
In this article, we will discuss learn how to expand (x + a)(x + b) and (x – a)(x – b) with some examples. It means the product of the variables and sum of constant terms and product of the constant terms. The expansion of the binomial product is nothing but the quadratic equation.
Express a² + b² + c² – ab – bc – ca as Sum of Squares
a² + b² + c² – ab – bc – ca are the sum of squares of three numbers and subtraction of product of two constant terms. We will the formula for a² + b² + c² with derivations and examples here. Learn the properties of a² + b² + c² – ab – bc – ca on this page. Just click on the provided links and practice the problems.
Simplification of (a + b)(a – b)
Simplification of (a + b)(a – b) is the multiplication of the two terms a and b. It is a binomial expression. The expansion of the binomial expression (a + b)(a – b) is the multiplication of each term and addition of it. Students who are confused about the simplification of (a + b)(a – b) can clarify their doubts with clear-cut explanations from our page.
Expansion of (a ± b)³
a and b are the two constant terms that mean it is considered as the binomial algebraic expression. a plus b whole cube is equal to a cube plus b cubed plus three times product of a squared b plus three times product of a and b square. The students can understand the concept of Expansion of (a ± b)³ by referring to our article.
Expansion of (x + a)(x + b)(x + c)
Expansion of (x + a)(x + b)(x + c) is the product of unknown variables and the constant terms. Expansion is nothing but multiplying each variable with the constant term and writing the result in the trinomial expression. In simple, we can say that it is the cubic of x, the sum of constant terms, and the product of the constant terms.
FAQs on Expansion of Powers of Binomials and Trinomials
1. How do you expand the power of a binomial?
To expand the power of binomial we have to identify the terms of the binomial positions and relate it to the formulas. By using the formulas we can expand the power of a binomial expression.
2. How do you expand powers?
While increasing power to power in the algebraic expression, we need to find the new power by multiplying the two powers together. There are some properties to multiply the powers and bases.
3. What is binomial and trinomial expressions?
An expression with two constant terms like a and b is known as binomial expression and the expression with three constant terms such as a, b, and c then it is known as the trinomial expression.