Question

Which one of the following identities does the given image represent?

• A. ${\text{(x+a)(x+b) = x}}^2+\mathrm{ax}+\mathrm{bx}+\mathrm{ab}$
• B. ${\text{(x+a)(x-b) = x}}^2+\mathrm{ax}-\mathrm{bx}-\mathrm{ab}$
• C. ${\text{(x-a)(x+b) = x}}^2\text{-}\mathrm{ax}+\mathrm{bx}-\mathrm{ab}$
• D. ${\text{(x-a)(x-b) = x}}^2\text{-}\mathrm{ax}-\mathrm{bx}+\mathrm{ab}$

Answer 1

The correct option is A ${\text{(x+a)(x+b) = x}}^2+\mathrm{ax}+\mathrm{bx}+\mathrm{ab}$


In the above image, the length and breadth of the given rectangle are (x+a) and (x+b).
Area of that rectangle is equal to the sum of area of a square whose area is $x^2$ and areas of 3 rectangles $ax$, $bx$ and $ab$.
So, $(x+a)(x+b)=x^2+ax+bx+ab$.