NJSLA Algebra II Arithmetic with Polynomials and Rational Expressions. Practice it free.

Multiply the coefficients: $6 \cdot 1 \cdot 2 = 12\textsf{.}$ Add the exponents on $m$ and on $n$: $m^{1+1} n^{1+1} = m^{2} n^{2}\textsf{.}$ So the product is $12m^{2}n^{2}\textsf{.}$

Distribute the minus sign: $(4x^2 - x + 6) - 2x^2 - 3x + 1\textsf{.}$ Combine $x^2$ terms: $4x^2 - 2x^2 = 2x^2\textsf{.}$ Combine $x$ terms: $-x - 3x = -4x\textsf{.}$ Combine constants: $6 + 1 = 7\textsf{.}$ Result: $2x^2 - 4x + 7\textsf{.}$

Expand: $(x + 3)(x + 3) = x^2 + 6x + 9$. Then subtract $9$: $x^2 + 6x + 9 - 9 = x^2 + 6x$.

$(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$; with $a = x$ and $b = 3$, this gives $x^{3} + 9x^{2} + 27x + 27$.

Multiply the coefficients: $3 \cdot 4 = 12\textsf{.}$ Add the exponents on $x$: $x^{2+1} = x^{3}\textsf{.}$ So the product is $12x^{3}\textsf{.}$

Distribute the minus sign: $(5x^2 + 3) - x^2 + 2x\textsf{.}$ Combine $x^2$ terms: $5x^2 - x^2 = 4x^2\textsf{.}$ The $x$ term is $2x\textsf{.}$ The constant stays $3\textsf{.}$ Result: $4x^2 + 2x + 3\textsf{.}$

Expand: $(x - 8)(x + 1) = x^2 + x - 8x - 8 = x^2 - 7x - 8$. Then add $7$: $x^2 - 7x - 8 + 7 = x^2 - 7x - 1$.

$(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$; with $a = 2x$ and $b = 1$, this gives $8x^{3} + 12x^{2} + 6x + 1$.