Question

a) What should be subtracted from $3x^2-4y^2+5xy+20$ to obtain $-x^2-y^2+6xy+20$?
b) Find the final expression when the algebraic expression $x^2+2xy+y^2$ is multiplied by $xy$. [4 MARKS]

Answer 1

Each option: 1.5 Marks

a) Let q be the expression to be subtracted.

Then according to the question,

$3x^2-4y^2+5xy+20-q=-x^2-y^2+6xy+20$

$\Rightarrow q=3x^2-4y^2+5xy+20-(-x^2-y^2+6xy+20)$

$\Rightarrow q=3x^2-4y^2+5xy+20+x^2+y^2-6xy-20$

$\Rightarrow q=3x^2+x^2-4y^2+y^2+5xy-6xy+20-20$

$\Rightarrow q=4x^2-3y^2-xy+0$

Hence, $4x^2-3y^2-xy$ should be subtracted from $3x^2-4y^2+5xy+20$ to obtain $-x^2-y^2+6xy+20$.

b) As per the question:
$x^2+2xy+y^2$ is multiplied by $xy$

So, $xy$$\times$ $x^2+2xy+y^2$

$=xy\times x^2+xy\times 2xy+xy\times y^2$

$=x^{2+1}y+2x^{1+1}{y}^{1+1}+x{y}^{1+2}$

$\because a^m\times a^n=a^{m+n}$

$=x^{3}y+2x^2{y}^2+x{y}^3$