Question

1. Multiply the following and write your answer in lowest terms

Answer 1

SOLUTION IS IN THE ATTACHMENT

RATIONAL EXPRESSIONS :
A rational number is defined as a quotient a/b, of two integers a and b and b ≠0.A rational expression is a quotient p(x) /q(x) of two Polynomials p(x) and q(x) ,where q(x) ≠0.
•When the numerator and denominator of a rational expression do not have any common factor except 1, the rational expression is said to be expressed in the lowest terms.
•To reduce a rational expression to the lowest terms, factorise the numerator and the denominator and cancel the factors which are common to both.
•MULTIPLICATION OF RATIONAL EXPRESSIONS : p(x)/q(x) × g(x)/h(x)

HOPE THIS WILL HELP YOU….

Answer 2

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Here ,

we used algebraic identities:

i ) a² - b² = ( a + b )( a - b )

ii ) a³ + b³ = ( a + b )( a² - ab + b² )

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1 ) x² - 16

= x² - 4²

= ( x + 4 )( x - 4 )

2 ) x³ + 64

= x³ + 4³

= ( x + 4 ) [ x² - 4x + 4² ]

= ( x + 4 )( x² - 4x + 16 )

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