Question

$\text{Ritika has a square flower garden of area}49a^2-81$ sq. m. On representing the above area in the simplest form, it will be equal to sq. m.

• A. (7a + 7)(9a - 9)
• B. (7a + 9)(7a - 9)
• C. (9a + 7)(7a - 9)
• D. (9a + 7)(9a - 7)

Answer 1

The correct option is B (7a + 9)(7a - 9)

Given

$\text{Area of the square flower garden}=49a^2-81sq.m.$

We observe:
$49a^2=7\times 7\times a\times a=(7a{)}^2$

${81}^2=9\times 9=(9{)}^2$

So, the area of the square garden can be expressed as:

$49a^2-81=(7a{)}^2-(9{)}^2$

$\text{We know,}{x}^2-y^2=(x+y)(x-y)$

$\text{So,}x=7aandy=9$

$\text{So,}49a^2-81=(7a+9)(7a-9)$