Monica Capoor Solutions for Chapter: Factorisation, Exercise 6: EXERCISE

Factorise the following algebraic expression.

$4x^2+12xy+9y^2-z^2$

Factorise the following algebraic expressions.

$25-a^2-2ab-b^2$

Upon factorising the following algebraic expressions, we get $\left(x^2+y^2+xy\right)\left(x^2+y^2+kxy\right)$, then find the value of $k$.

$x^4+y^4+x^2{y}^2$

If the factors of the algebraic expression $x^4+x^2+1$ is $\left(x^a+x+b\right)\left(x^a-x+b\right)$, then find the value of $a+b$.

[Hint: Add and subtract $x^2$]

If the factors of the algebraic expression $x^2+4$ is $\left(x^a+2x+b\right)\left(x^a-2x+b\right)$, then find the value of $a+b$.

[Hint: Add and subtract $4x^2$]

Evaluate ${\left(203\right)}^2-{\left(197\right)}^2$

${\left(6.6\right)}^2-{\left(3.4\right)}^2=?$

Simplify: $\frac{0.75\times 0.75-0.25\times 0.25}{0.75-0.25}$