Name: Using Algebraic Expressions-Formulas
Uploaded: 2019-07-19
Duration: 6 min 2 s
Description: With this video you'll learn how formulas in mathematics are written in a concise and general form using algebraic expressions with the examples on perimeter...

Question

Fill in the boxes with algebraic expressions to create magic square.

		$- 4 t + 5 u$
		$- 2 (- 3 t - 2 u)$
		$- 5 (t - 3 u)$

Accepted Answer

Given magic square:

$- 4 t + 5 u$

$- 2 (- 3 t - 2 u)$

$- 5 (t - 3 u)$

We know that in the magic square the sum of the numbers in each row, column and diagonal is three times to middle number.

Means the sum of the numbers in each row, column, and diagonal is: $- 4 t + 5 u - 2 (- 3 t - 2 u) - 5 (t - 3 u) = - 3 t + 24 u$

So, the value of the middle term is: $\frac{- 3 t + 24 u}{3} = - t + 8 u$

Now, we can easily find the missing terms. By assuming $at + bu$ in different rows and columns at different times. And putting the sum of the numbers in each row, column, and diagonal is $- 3 t + 24 u$ .

Now, we take row2:

$a t + b u - t + 8 u - 2 (- 3 t - 2 u) = - 3 t + 24 u a t + b u - t + 8 u + 6 t + 4 u = - 3 t + 24 u (a - 1 + 6) t + (b + 8 + 4) u = - 3 t + 24 u n o w c o m p a i r i n g b o t h s i d e a - 1 + 6 = - 3 a n d b + 8 + 4 = 24 a = - 8 a n d b = 12$

So, the value of row2, column1 is $- 8 t + 12 u$

Now, we take diagonal1:

$a t + b u - t + 8 u - 5 (t - 3 u) = - 3 t + 24 u a t + b u - t + 8 u - 5 t + 15 u = - 3 t + 24 u (a - 1 - 5) t + (b + 8 + 15) u = - 3 t + 24 u n o w c o m p a i r i n g b o t h s i d e a - 1 - 5 = - 3 a n d b + 8 + 15 = 24 a = 3 a n d b = 1$

So, the value of row1, column1 is $3 t + u$

Now, we take column1:

$3 t + u - 8 t + 12 u + a t + b u = - 3 t + 24 u (3 - 8 + a) t + (1 + 12 + b) u = - 3 t + 24 u n o w c o m p a i r i n g b o t h s i d e 3 - 8 + a = - 3 a n d 1 + 12 + b = 24 a = 2 a n d b = 11$

So, the value of row3, column1 is $2 t + 11 u$

Now, we take row1:

$3 t + u + a t + b u + - 4 t + 5 u = - 3 t + 24 u (3 + a - 4) t + (1 + b + 5) u = - 3 t + 24 u n o w c o m p a i r i n g b o t h s i d e 3 + a - 4 = - 3 a n d 1 + b + 5 = 24 a = - 2 a n d b = 18$

So, the value of row1, column2 is $- 2 t + 18 u$

Now, we take column2:

$- 2 t + 18 u - t + 8 u + a t + b u = - 3 t + 24 u (- 2 - 1 + a) t + (18 + 8 + b) u = - 3 t + 24 u n o w c o m p a i r i n g b o t h s i d e - 2 - 1 + a = - 3 a n d 18 + 8 + b = 24 a = 0 a n d b = - 2$

So, the value of row3, column2 is $- 2 u$

So, the complete magic square is:

$3 t + u$ $- 2 t + 18 u$ $- 4 t + 5 u$

$- 8 t + 12 u$ $- t + 8 u$ $- 2 (- 3 t - 2 u)$

$2 t + 11 u$ $- 2 u$ $- 5 (t - 3 u)$

Fill in the boxes with algebraic expressions to create magic square.

$- 4 t + 5 u$

$- 2 (- 3 t - 2 u)$

$- 5 (t - 3 u)$

Important Questions on Algebraic Expressions and Equations Puzzles and Tricks

Learn and Prepare for any exam you want !

Fill in the boxes with algebraic expressions to create magic square. -4t+5u -2(-3t-2u) -5(t-3u)

Important Questions on Algebraic Expressions and Equations Puzzles and Tricks

Learn and Prepare for any exam you want !

Fill in the boxes with algebraic expressions to create magic square.

$- 4 t + 5 u$

$- 2 (- 3 t - 2 u)$

$- 5 (t - 3 u)$