write down the following products .
1. (5p square-7q) (5p square+7q)
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Answers
Step-by-step explanation:
• Terms are formed by the product of variables and constants, e.g.
–3xy, 2xyz, 5x2, etc.
• Terms are added to form expressions, e.g. –2xy + 5x2.
• Expressions that contain exactly one, two and three terms are
called monomials, binomials and trinomials, respectively.
• In general, any expression containing one or more terms with nonzero coefficients (and with variables having non-negative exponents)
is called a polynomial.
• Like terms are formed from the same variables and the powers of
these variables are also the same. But coefficients of like terms
need not be the same.
• There are number of situations like finding the area of rectangle,
triangle, etc. in which we need to multiply algebraic expressions.
• Multiplication of two algebraic expressions is again an algebraic
expression.
• A monomial multiplied by a monomial always gives a monomial.
• While multiplying a polynomial by a monomial, we multiply every
term in the polynomial by the monomial using the distributive
law a ( b + c) = ab + ac.
12/04/18
• In the multiplication of a polynomial by a binomial (or trinomial),
we multiply term by term, i.e. every term of the polynomial is
multiplied by every term in the binomial (or trinomial) using the
distributive property.
• An identity is an equality, which is true for all values of its variables
in the equality, i.e. an identity is a universal truth.
• An equation is true only for certain values of its variables.
• Some standard identities:
(i) (a + b)
2 = a2 + 2ab + b2
(ii) (a – b)
2 = a2 – 2ab + b2
(iii) (a + b) (a – b) = a2 – b2
(iv) (x + a) (x + b) = x2 + (a + b) x + ab
(ii) Factorisation
• Representation of an algebraic expression as the product of two or
more expressions is called factorisation. Each such expression is
called a factor of the given algebraic expression.
• When we factorise an expression, we write it as a product of its
factors. These factors may be numbers, algebraic (or literal) variables
or algebraic expressions.
A formula is an equation stating a relationship between two or more
variables. For example, the number of square units in the area (A) of a
rectangle is equal to the number of units of length (l) multiplied by the
number of units of width (w). Therefore, the formula for the area of a
rectangle is A = lw.
Sometimes, you can evaluate a variable in a formula by using the given
information.