MATHS PROJECT

Made by :- shubhamClass:- viii-c

ALGEBRAIC EXPRESSION

AND IDENTITIES

INDEX• Expression • Term, factors and coefficient• Monomial, binomials and polynomials • Like and unlike terms• Addition and subtraction in algebra• Multiplication in algebra• What is an identity?• Applying identities

Expression• Numbers, symbols and operators (such as + and ×)

grouped together that show the value of something. Example: 2×3 is an expression

Terms, factors and coefficientTerms :- In Algebra a term is either a single number or

variable, or numbers and variables multiplied together. Terms are separated by + or − signs

Factors :-Factors are numbers you can multiply together to get another number: Example: 2 and 3 are factors of 6, because 2 × 3 = 6. A number can have MANY factors!

Example: What are the factors of 12? 3 and 4 are factors of 12, because 3 × 4 = 12. Also 2 × 6 = 12 so 2 and 6 are also factors of 12. And 1 × 12 = 12 so 1 and 12 are factors of 12 as well.In Algebra, factors are what you can multiply together to get an expression. (x+3) and (x+1) are factors of x2 + 4x + 3:

• Coefficient :-A number used to multiply a variable.Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient.

Sometimes a letter stands in for the number.

Example: In ax2 + bx + c, "x" is a variable, and "a" and "b" are coefficients.

Monomial, binomial and polynomial• Monomial :- A polynomial with just one term.

Example: 3x2

Binomial :- A polynomial with two terms. Example: 3x2 + 2Polynomial :-An expression that can have constants, variables and exponents, that can be combined using addition, subtraction, multiplication and division, but:• no division by a variable.• a variable's exponents can only be 0,1,2,3,... etc.• it can't have an infinite number of terms.

Like and unlike terms• Like terms:- "Like terms" are terms whose variables (and

their exponents such as the 2 in x2) are the same.In other words, terms that are "like" each other.

• Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.

Example: 7x + x -2x

Are all like terms because the variables are all x Example:(1/3)xy2-2xy2+6xy2

Are all like terms because the variables are all xy2

• Unlike terms :-if they are not like terms, they are called "Unlike Terms":

Combining like terms• You can add like terms together to make one term: Example: 7x + x They are both like terms, so you can just add them: 7x + x = 8x

• By the way ... why don't we write "1x" ? It is just easier to write x. Imagine you were adding eggs:• 7 eggs plus 1 egg is 8 eggs could be written 7 eggs + egg = 8 eggs Example: 3x2 - 7 + 4x3 - x2 + 2 Some of the terms are like terms. Combine like terms:(3x2 - x2) + (4x3) + (2 - 7) Then add like terms: 2x2 + 4x3 - 5

Addition and subtraction in algebra

• Addition of algebraic expressions :- while adding algebraic expression we collect the

like terms and add them. The sum of several like terms is the like terms whose coefficient is the sum

of the coefficient of these like terms. example :-add: 6a+8b-5c and 2b+c-4a.Answer:- collecting like terms 6a-4a+8b+2b-5c+c :-> 2a+10b-4c

• Subtraction of algebraic expressions :- steps for subtraction of algebraic expressions:-i. arrange the terms of the given expression in the

same order.ii. Write the given expressions in such a way that the

like terms occur one below the other, keeping the subtracted in the second row.

iii. Change the sign of each term in the lower row from+ to – and – to +

iv. With new signs of the terms of lower row, add column wise

• Example :- subtract 4a+5b-3c from 6a- 3b+c answer :-we have 6a-3b+c +4a+5b-3c - - + 2a-8b+4c

Multiplication and division in algebra

• Before taking up the product of algebraic expressions. Let us look at 2 important rules

i. The product of 2 factors with the same signs is positive and factors with different signs is negative.

ii. If x is a variable and m and n are positive integers, then (xᴹ × xᴺ)=x(ᴹ+ᴺ)

Multiplication of two monomials• Rule :- product of 2 monomials (product of their numerical coefficient)×(product

of their variable parts) example :- find the product of (6xy)×(-3xᶾyᶾ)Answer:- (6×-3) × (xy × xᶾyᶾ) = -18x⁴y⁴

Multiplication of a polynomial by a monomial

• Rule :-multiply each term of the polynomial by the monomial, using the distributive law

a×(b+c)=a ×b+a ×c

Multiplication of two binomials