Algebraic Identities

The expanded form of

 $\left(4h-3k\right)^2$  is______

•  $16h^2+24hk+9k^2$  

•  $16h^2-24hk+9k^2$  

•  $16h^2+24hk-9k^2$  

•  $16h^2-24hk-9k^2$  

Which one of the following can be read as

"The difference of two squares"?

• $\left(a+b\right)^2$

• $\left(a-b\right)^2$

• $a^2-b^2$

• $a^2+b^2$

Which of the following expressions will result as

 $16x^2-25y^2$ after expansion ?

•  $\left(4x+5y\right)\left(4x+5y\right)$  

•  $\left(4x-5y\right)\left(4x+5y\right)$  

•  $\left(4x-5y\right)\left(4x-5y\right)$  

•  $\left(4x-5y\right)^2$  

Which of the following expressions CAN NOT be solved with the identity

 $\left(a+b\right)^2=a^2+2ab+b^2$  ?

•  $\left(2a+3b\right)^2$  

•  $\left(2a+3b\right)\left(2a+3b\right)$  

•  $\left(3a+2b\right)\left(3a+2b\right)$  

•  $\left(3a+2b\right)\left(3a-2b\right)$  

Which of the following identities can be used for solving

 $\left(\frac{2a}{3b}-\frac{5c}{7}\right)\left(\frac{2a}{3b}-\frac{5c}{7}\right)$  ?

•  $\left(a+b\right)\left(a-b\right)=a^2-b^2$  

•  $\left(a+b\right)^2=a^2+2ab+b^2$  

•  $\left(a-b\right)^2=a^2-2ab+b^2$  

• None of them

Which of the following statement is the best explanation of the identity

 $\left(a+b\right)^2=a^2+2ab+b^2$  ?

• The square of the sum of two numbers

• The square of the difference of two numbers

• The sum of squares of two numbers

• The difference of the square of two numbers

 $\left(\frac{2m}{3}-\frac{3n}{2}\right)^2=$  ________

•  $\frac{4m}{2}+2mn+\frac{9n}{4}$  

•  $\frac{4m^2}{2}+2mn+\frac{9n^2}{4}$  

•  $\frac{4m^2}{9}+2mn+\frac{9n^2}{4}$  

•  $\frac{4m^2}{9}-2mn+\frac{9n^2}{4}$  

Expanded form of

 $\left(4x-5\right)\left(4x+5\right)$  is __________

•  $4x^2-25$  

•  $4x^2+25$  

•  $16x^2+25$  

•  $16x^2-25$  

The square of

 $x^2-2y^2$  is _________

•  $x^4+4y^4$  

•  $x^4-4y^4$  

•  $x^4-4x^2y^2+4y^4$  

•  $x^4-4x^2y^2-4y^4$  

 $\left(x^2-y^2\right)\times\left(x^2+y^2\right)=$  ____________

•  $2x^2+2y^2$  

•  $x^4-y^4$  

•  $2x^2-2y^2$  

•  $x^4+y^4$