Question

Match the following.

• A. $x^2-36$
• B. $x^2+8x+15$
• C. $16x^2+9y^2-24xy$
• D. $x^2+25y^2+10xy$

Answer 1

Case 1:
$(4x-3y{)}^2$
Using the identity $(a-b{)}^2=a^2+b^2-2ab$,
$(4x-3y{)}^2=(4x{)}^2+(3y{)}^2-2\times 4x\times 3y$
$\Rightarrow (4x-3y{)}^2=16x^2+9y^2-24xy$

Case 2:
$(x+5y{)}^2$
Using the identity $(a+b{)}^2=a^2+b^2+2ab$,
$(x+5y{)}^2=(x{)}^2+(5y{)}^2+2\times x\times 5y$
$\Rightarrow (x+5y{)}^2=x^2+25y^2+10xy$

Case 3:
$(x+6)(x-6)$
Using the identity $(a+b)(a-b)=a^2-b^2$,
$(x+6)(x-6)=(x{)}^2-(6{)}^2$
$\Rightarrow (x+6)(x-6)=x^2-36$

Case 4:
$(x+3)(x+5)$
Using the identity $(x+a)(x+b)=x^2+(a+b)x+ab$,
$(x+3)(x+5)=x^2+(3+5)x+3\times 5$
$\Rightarrow (x+3)(x+5)=x^2+8x+15$