M L Aggarwal Solutions for Chapter: Algebraic Expressions and Identities, Exercise 4: Check Your Progress

Using suitable identity, evaluate the following:

$201\times 199$

Using suitable identities, evaluate the following:

${87}^2-{13}^2$

Using suitable identities, evaluate the following:

$105\times 107$

Prove the following:

$(a+b{)}^2=(a-b{)}^2+4ab$

Prove the following:

$(2a+3b{)}^2+(2a-3b{)}^2=8a^2+18b^2$

If $x+\frac{1}{x}=5$, evaluate $x^2+\frac{1}{x^2}$

If $x+\frac{1}{x}=5$, evaluate $x^4+\frac{1}{x^4}$

If $a+b=5$ and $a^2+b^2=13$, find $ab$.