(a) Here \(\displaystyle{b}{<}{0}\Rightarrow−{b}\)</span> will be a positive number.

Thus, sign of -a is positive.

(b) It is known that product of two negative number will be positive.

As \(\displaystyle{b}{<}{0}{\quad\text{and}\quad}{c}{<}{0}\Rightarrow{b}{c}{>}{0}.\)

Thus, sign of bc is positive.

So a and bc positive.

It is known that sum of two positive number will be positive.

Thus, a+bc>0.

Thus, sign of a + bc is positive.

(c) It is known that when a positive number is subtracted from a negative number, the resultant number will be negative .

Here \(\displaystyle{a}{>}{0},{c}{<}{0}\Rightarrow{c}−{a}{<}{0}\)</span>.

Thus, sign of a-b is negative .

(d) The square of ay number will be positive. Thus, \(\displaystyle{b}^{{2}}{>}{0}\) and given a>0.

Thus, \(\displaystyle{a}{b}^{{2}}{>}{0}\).

Therefore, the sign of \(\displaystyle{a}{b}^{{2}}\) is positive.

Thus, sign of -a is positive.

(b) It is known that product of two negative number will be positive.

As \(\displaystyle{b}{<}{0}{\quad\text{and}\quad}{c}{<}{0}\Rightarrow{b}{c}{>}{0}.\)

Thus, sign of bc is positive.

So a and bc positive.

It is known that sum of two positive number will be positive.

Thus, a+bc>0.

Thus, sign of a + bc is positive.

(c) It is known that when a positive number is subtracted from a negative number, the resultant number will be negative .

Here \(\displaystyle{a}{>}{0},{c}{<}{0}\Rightarrow{c}−{a}{<}{0}\)</span>.

Thus, sign of a-b is negative .

(d) The square of ay number will be positive. Thus, \(\displaystyle{b}^{{2}}{>}{0}\) and given a>0.

Thus, \(\displaystyle{a}{b}^{{2}}{>}{0}\).

Therefore, the sign of \(\displaystyle{a}{b}^{{2}}\) is positive.