Algebraic Expressions and Identities

Subtract $(w - 10)$ from $(w + 10)$.

Simplify: $12h - 2h - h$.

What is the result of subtracting $3x$ from $(10 - x)$?

Find the sum: $(3x + 3y) + (x - y)$.

Subtract $5a - 2b + 3c$ from $2a + b - c$.

Add the polynomials: $(x^3 + x^2 + x + 1)$ and $(x^3 - x^2 + x - 1)$.

Simplify the expression: $7x - [2y - (3x + 4y)]$.

Subtract $(x^2 - 3x + 2)$ from the sum of $(2x^2 + 5)$ and $(x - 7)$.

If $A = x - y$, $B = y - z$, and $C = z - x$, find the result of $(A - B) - (B - C)$.

Subtract the sum of $(\frac{1}{2}x^2 + \frac{1}{3}xy)$ and $(\frac{1}{4}x^2 - \frac{1}{6}xy)$ from $x^2 + xy$.

Find the product of $(a - b)$ and $b$.

What is the result of $1 \times (4a - 5b)$?

Multiply the binomials $(x - y)$ and $(z + w)$.

Calculate the result: $8x \times 0.25x$.

Expand the product of three factors: $x(x + 1)(x + 2)$.

Expand: $(a + b)(a + b)$.

Find the product: $(2x - 1)(x^2 + x + 1)$.

Multiply the trinomial $(x^2 - 2x + 4)$ by the binomial $(x + 2)$.

What is the constant term in the product $(x - 1)(x + 2)(x - 3)(x + 4)$?

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

What is the square of $(3x - 1)$?

Calculate $103 \times 97$ using a standard identity.

The expression $4x^2 - 12x + 9$ is equivalent to:

Expand $(a - 0.5)^2$.

What must be added to $49x^2 + 64y^2$ to make it a perfect square $(7x+8y)^2$?

Simplify $(3x+2y)^2 + (3x-2y)^2$.

Which identity is best to evaluate $995 \times 1005$?

Simplify the following expression by applying suitable algebraic identities: $(2x + 5y)^2 - 2(4x^2 - 25y^2) + (2x - 5y)^2$

Expand $(\frac{x}{y} - 1)^2$.

If $a^2 + b^2 = 25$ and $a - b = 1$, find the area of a rectangle with sides $a$ and $b$.

Simplify $(10x - 0.1)^2$ using the identity $(a-b)^2 = a^2 - 2ab + b^2$.

Expand $(0.1p + 0.2q)^2$ using identities.

Find the square of $(\frac{2}{3}x + 9)$ using $(a+b)^2$.

Calculate $503 \times 507$ using $(x+a)(x+b) = x^2 + (a+b)x + ab$.

If $x - \frac{1}{x} = 8$, find the value of $x^2 + \frac{1}{x^2}$.

Expand the expression $(x^2 + y^2)^2$.

Expand the expression $(3a - 0.5b)^2$.

If $x + y = 5$ and $x - y = 3$, find the value of $x^3y - xy^3$.

Evaluate the value of the fraction $\frac{103^2 - 97^2}{120}$ using identities.

If $a - b = 0.5$ and $a + b = 4.2$, find the value of $a^2 - b^2$.