Expand the following using a suitable identity:

$(\mathrm{x}+1)(\mathrm{x}-1)$

If $x$ is a natural number.

If $x^2+ax+b$ is a perfect square, prove that $a^2=4b$.

If $x$ is a natural number.

If $x^2+ax+16$ is a perfect square number, then which number is $a$?

Solve the given equation and verify the answer:

$\frac{2x}{5}-\frac{3}{2}=\frac{x}{2}+1$

Find the product of $\left(x+3\right)\left(x-3\right)$.

Solve the following equation and verify the answer:

$\frac{3}{4} (x-1)=x-3$

Expand: ${\left(8a+3b\right)}^2$.

Pick out the solution from the values given in the bracket next to each equation.

Show that the other values do not satisfy the equation.
$5m=60 (10,5,12,15)$

Find the product of $\left(x+6\right)\left(x+6\right)$.

Solve the following equation and verify the answer:

$5(x-1)+2(x+3)+6=0$

Solve the following equation and verify the answer:

$6(1-4x)+7(2+5x)=53$

Solve the following equation and verify the answer:

$3(2-5x)-2(1-6x)=1$