Standard Identities in Algebra

If ${\left(x-y\right)}^2=4-4y+y^2$, then let's find the value of $x$.

Write the expression which when added to $a^2+4$ gives a whole number.

Find: $592\times 608$

Consider, the special case of identity $(x+a)(x+b)=x^2+(a+b)x+ab$ with$b=-a$, what do you get? Is it related to identity, $\left(a+b\right)\left(a-b\right)=a^2-b^2$?

Consider, the special case of Identity $(x+a)(x+b)=x^2+(a+b)x+ab$ with $a=-c$ and $b=-c$. What do you get? Is it related to Identity ${\left(a-b\right)}^2=a^2-2ab+b^2$?

Verify the identity, $(x+a)(x+b)=x^2+(a+b)x+ab$, for $a=2,b=3,x=5$.

If two expressions are equal for all the values of same parameter, then the statement of equality between the two expressions is called an identity.

Check whether given one is identity or equation?

${\left(\mathrm{a}+\mathrm{b}\right)}^2={\mathrm{a}}^2+2\mathrm{ab}+{\mathrm{b}}^2$

The product of $\left(\frac{4}{3}{x}^2+3\right)\left(\frac{4}{3}{x}^2+3\right)$ is $\frac{16}{9}{x}^4+8x^2+k$. Find $k$.

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

$(a+b{)}^2=a^{\text{k}}+2ab+b^{\text{k}}$

The value of k is _____.

Using the identity $(x+a)(x+b)=x^2+x(a+b)+ab$. If the product of $(8+pq)(pq+7)$ $p^2{q}^2+kpq+56$, find the value of $k$.

Factorize $\left(k^2-36\right)$.

If ${\left(\mathrm{x}+\frac{1}{2}\right)}^2=a{\mathrm{x}}^2+\frac{1}{b}+c\mathrm{x}$, find $a+b+c$.

Expand by using identity.

If ${\left(7\mathrm{m}-4\right)}^2=a{\mathrm{m}}^2+b+c\mathrm{m}$, find $a+b+c$.