Suppose 7x is split as 2x + 5x; can a similar rectangular arrangement be formed? Consider other possibilities Class 9

Suppose 7x is split as 2x + 5x; can a similar rectangular arrangement be formed? Consider other possibilities Class 9

Question 1.

Suppose 7x is split as 2x + 5x; can a similar rectangular arrangement be formed? Consider other possibilities and check. Class 9

Answer:

Suppose 7x is split as 2x + 5x.

Then,

x² + 7x + 12 = x² + 2x + 5x + 12

To form a rectangular arrangement using algebra tiles, the unit tiles must fit exactly into rows and columns matching the split numbers.

Here, 12 unit tiles would need to form a

2 × 5 array, but:

2 × 5 = 10 ≠ 12

So, a similar rectangular arrangement cannot be formed.

Other possibilities for splitting 7x:

7x = 1x + 6x, 2x + 5x, 3x + 4x

Check products:

i. 1 × 6 = 6

ii. 2 × 5 = 10

iii. 3 × 4 = 12

Only 3x + 4x gives product 12.

Hence, only the split:

7x = 3x + 4x

forms a proper rectangular arrangement. Thus, algebra tiles can be used to represent products and find factors of algebraic expressions.