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example multiply 3x5 4x3 2x - 1 and x4 2x2 4the product is given by3x5 x4 2x2 4 4x3 x4 2x2 4 2x x4 2x2 4 - 1 x4
example 1add 4x4 3x3 - x2 x 6 and -7x4 - 3x3 8x2 8x - 4we write them one below the other as shown below 4x4
binomials trinomials and polynomials which we have seen above are not the only type we can have them in a single variable say
case 1 suppose we have two terms 8ab and 4ab on dividing the first by the second we have 8ab4ab 2 or 4ab8ab 12 depending on whether we consider
the product on multiplying - 4bc with 2a is - 8abc that is a term with minus sign multiplied with a term having a positive term gives a product which
the product of -7ab and 3ab is -7 x 3 a2 b2 -21a2 b2 in other words a term with minus sign when multiplied with a term having a positive
case 1 suppose we have two terms 7ab and 3ab when we multiply these two terms we get 7ab x 3ab 7 x 3 a1 1 b1 1 therefore
in this case the first point we have to remember is that we do not get a single value when we add two or more terms which are unlike in
suppose we are required to find the difference between 3abc and 7abc we look at two scenarios the value we would obtain by subtracting a
case 1 suppose we are given expressions like 3abc and 7abc and asked to compute their sum if this is the case we should not worry much
in arithmetic we deal with numbers in contrast to this in algebra we deal with symbols these symbols are often represented by lower case
example reduce 2436 to its lowest terms 243612186923 in the first step we divide the numerator and the denominator by 2 the
example find the highest common factor of 54 72 and 150first we consider 54 and 72 the hcf for these two quantities is calculated as
we know that a factor is a quantity which divides the given quantity without leaving any remainder similar to lcm above we can find
at times we consider only the magnitude of the number without attaching much importance to its direction under these circumstances the
intervals which extend indefinitely in both the directions are known as unbounded intervals these are written with the aid of symbols
let a and b be fixed real numbers such that a lt b on a number line the different types of intervals we have arethe open interval
here we look at only the rules without going into their proofs they area lt b if and only if b - a gt 0if a lt b
what inequalities and intervals are if it is given that a real number p is not less than another real number q we understand that either
all the number sets we have seen above put together comprise the real numbers real numbers are also inadequate in the sense that it does
the set of whole numbers also does not satisfy all our requirements as on observation we find that it does not include negative numbers
observe that natural numbers do not have a zero this shortcoming is made good when we consider the set of whole numbers the
to begin with we have counting numbers these numbers are also known as natural numbers and are denoted by a symbol n these