Factorise of the following : $27 y^{3}+125 z^{3}$
Factorise of the following : $27 y^{3}+125 z^{3}$
Using the identity $\left(x^{3}+y^{3}\right)=(x+y)\left(x^{2}-x y+y^{2}\right),$ we have
$27 y^{3}+125 z^{3} =(3 y)^{3}+(5 z)^{3}=(3 y+5 z)\left[(3 y)^{2}-(3 y)(5 z)+(5 z)^{2}\right]$
$=(3 y+5 z)\left(9 y^{2}-15 y z+25 z^{2}\right)$
Similar Questions
Which of the following expressions are polynomials in one variable and which are not ? State reasons for your answer. $3 \sqrt{t}+t \sqrt{2}$
Which of the following expressions are polynomials in one variable and which are not ? State reasons for your answer. $3 \sqrt{t}+t \sqrt{2}$
Classify the following as linear, quadratic and cubic polynomials :
$(i)$ $x^{2}+x$
$(ii)$ $x-x^{3}$
$(iii)$ $y+y^{2}+4$
Classify the following as linear, quadratic and cubic polynomials :
$(i)$ $x^{2}+x$
$(ii)$ $x-x^{3}$
$(iii)$ $y+y^{2}+4$
Examine whether $x+2$ is a factor of $x^{3}+3 x^{2}+5 x+6$ and of $2 x+4$.
Examine whether $x+2$ is a factor of $x^{3}+3 x^{2}+5 x+6$ and of $2 x+4$.
Check whether $-2$ and $2$ are zeroes of the polynomial $x + 2$.
Check whether $-2$ and $2$ are zeroes of the polynomial $x + 2$.
Find the zero of the polynomial : $p(x)=c x+d, \,c \neq 0, \,c,\,d$ are real numbers.
Find the zero of the polynomial : $p(x)=c x+d, \,c \neq 0, \,c,\,d$ are real numbers.