Please solve all part clearly Explain Why a constant monomia

Explain Why a constant monomial k does not have a degree if k - 0 otherwise the degree of k will be 0 Using the number line, explain why adding two positive numbers always gives a positive number while adding two negative numbers always gives a negative number. Analogously, in adding two numbers with different signs, the sign of the result always depends on the sign of the greater number. You may use examples to illustrate your explanation. When we square a product, we square each factor in the product. For example, . (3b)^2 = 9b^2. Explain why we cannot square a sum by simply squaring each term of the sum.

Solution

1.Monomial is a polynomial of single term .

here p(x) = c (constant ) degree of the polynomial =0

2 . consider the number line -------------------------------0---i----i---3---i---i----i----7------------

when we add 3 and 4 ,it means 3 and 4 more . when we mark it on the no line , mark 3 and then 4 parts we get the total =7

when we operate - 3 , -4 we subtract 4 from 3 . mark it on the no line

----------------------- -7 ------------ -3 ------0 -------------

( subtraction means proceeding left of -3 by 4 parts )

when we operate 4 , -3

-------------------------------0-----1---------------4----------- from 4 we proceed to the left of 4 by 3parts

we get 1 as the result

when we operate 3 , -4

----------------------------- -1-------0-----------------3------------------------- from 3 we proceed to the left by 4 parts and we get -1 as th result

3 . when we square the operation is (ab) (ab) = a b xab = a² b²

when we square the sum the operation is (a+b)² = (a+b) (a+b) = a²+ab+ba +b^{2 (distributive property )}

= a²+2ab+b²