Algebra Play

What is the result of $(x+y) - (x-y)$?

Solve for $x$: $2x - 3 = 7$.

Factorise $z^2 - 49$.

What is the area of a rectangle with length $3x$ and breadth $2y$?

Factorize the algebraic expression $a^2 - b^2 - a - b$ completely.

Evaluate the following expression using algebraic identities: $\frac{198 \times 198 - 102 \times 102}{96}$

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is $\frac{3}{2}$. What is the original rational number?

Find the value of $Q$ in the following: $31Q + 1Q3 = 501$.

If $x^2 + \frac{1}{x^2} = 27$, find the value of $x - \frac{1}{x}$.

The sum of three consecutive multiples of 11 is 363. Find the largest multiple.

Think of a number $x$. Add $50$. Subtract $50$. What is the result?

If you think of a number $n$, what is $3(n + 2) - 6$?

Think of a number $x$. Multiply by $2$. Add $8$. Divide by $2$. Subtract $4$. What is the result?

Think of a number $x$. Add $1$. Subtract $1$. Add $1$. Subtract $1$. What is the result?

Two-thirds of a number $x$ is equal to $6$. What is the value of $x$?

Think of a number $x$. Multiply it by $5$, add $15$, and divide the whole expression by $5$. If you then subtract $3$, what is the result?

A number $x$ minus $7$ is equal to twice the number minus $15$. What is $x$?

Think of a number $n$. Multiply by 8, add 16, divide by 4, subtract 4. What is the result?

A two-digit number $10x + y$ is added to its reversal $10y + x$. The sum is divided by 11. What is the quotient?

In the trick: Think of $x$, multiply by 5, add 20, divide by 5, subtract 4. The result is always $x$. If the first step was 'multiply by 4', what would the second step need to be to keep the result as $x$ after 'divide by 4' and 'subtract 4'?

In a 3-layer pyramid, the bottom row is $a, a, a$. What is the top block expression?

If the top block is $14$ and one bottom block is $x+1$, find the other bottom block if $x=3$.

The bottom row of a 3-layer pyramid is $2, 3, 2$. What is the top block?

If the bottom blocks are $x$ and $2x$, and the top is $15$, what is $x$?

In a three-layer pyramid, if all blocks in the bottom row are equal to $k$, what is the top block?

In a two-layer pyramid, if the base blocks are $2a+b$ and $a-2b$, what is the top block?

If the bottom row of a three-layer pyramid is $5, -2, 5$, what is the value of the top block?

In a 3-level pyramid, the bottom row is $x, 2x, x$. If the top block is 100, find $x$.

A 5-level pyramid has bottom row $x, 1, 1, 1, 1$. If the top block is 20, find $x$.

In a 4-level pyramid, the bottom row is $2, 3, 4, x$. If the top block is 35, find $x$.

In a grid pattern, if the $n$-th row has $n$ squares, how many squares are in the first 4 rows total?

In a $3 \times 3$ grid of consecutive numbers, if the top-left number is $1$, what is the sum of the diagonal from top-left to bottom-right?

In a grid where each row has 7 numbers (like a calendar), what is the number directly below $n$?

If three consecutive integers have a sum of $51$, the integers are:

In a $3 \times 3$ magic square, if the center number is 10, what is the sum of all nine numbers in the square?

A number of the form $10a + b$ is subtracted from $10b + a$ to get 54. What is the value of $b - a$?

In a $3 \times 3$ grid from a calendar, if the sum of the horizontal middle row is $H$ and the sum of the vertical middle column is $V$, which of the following is always true about $H$ and $V$?

An $8 \times 8$ chessboard grid has a total of how many squares of all sizes?

A square $ABCD$ on a grid has $A(1,1)$ and $B(4,1)$. What is the area of this square?

In a grid of numbers where $a_{i,j} = i+j$, what is the sum of all elements in a $n \times n$ grid?

Simplify: $(2x + 1)(2x - 1)$.

If the sum of two numbers is $2$, what is the maximum product?

What is the product of $1.1x$ and $1.1x$?

Evaluate $102 \times 98$ using algebra.

Find the maximum product of three integers that sum to $21$.

If $a + b = 10$, the product $ab$ is $21$. What is the value of $(a - b)^2$?

What is the difference between $(x+5)^2$ and $(x+4)(x+6)$?

If $x, y$ are positive integers such that $x + y = 12$, find the maximum value of $x^2 y$.

What is the minimum value of $x + y$ if $xy = 100$ and $x, y$ are positive real numbers?

Find the maximum value of $xy$ if $x + y = 10$ and $x$ must be an integer while $y$ can be any real number.

If $a, b, c$ are digits of a 3-digit number $abc$ divisible by $9$, then what can be said about $(a+b+c)$?

Which digit is at the units place of any number divisible by $5$ but not by $10$?

If $12x$ is divisible by $10$, what is the value of $x$?

What is the remainder when $99$ is divided by $9$?

Find the value of $x + y$ if $1x5y$ is the smallest four-digit number divisible by both $5$ and $10$.

If $B + B = B$, then the digit $B$ must be:

The number $1000a + 100b + 10c + d$ is the generalized form of which four-digit number?

A 4-digit number $3a4b$ is divisible by 9 and 10. Find the digit $a$.

In the cryptarithm $A + B + C = BC$, if $A, B, C$ are non-zero digits and $B=1$, find $A$.

The number $10x + y$ is divisible by 3. If $x + y = 12$, what is the minimum value of $x$?