HSA.APR.A.1 math practice. Learn by doing.

Multiply the coefficients: $5 \cdot 3 = 15\textsf{.}$ Add the exponents on $x$: $x^{1+1} = x^{2}\textsf{.}$ So the product is $15x^{2}\textsf{.}$

Distribute the minus sign: $(5x^2 + 3x + 2) - 2x^2 + 5\textsf{.}$ Combine $x^2$ terms: $5x^2 - 2x^2 = 3x^2\textsf{.}$ The $x$ term stays $3x\textsf{.}$ Combine constants: $2 + 5 = 7\textsf{.}$ Result: $3x^2 + 3x + 7\textsf{.}$

Expand: $(x + 2)(x + 5) = x^2 + 5x + 2x + 10 = x^2 + 7x + 10$. Then add $3$: $x^2 + 7x + 10 + 3 = x^2 + 7x + 13$.

$(x - 4)^{2} = x^{2} - 2(x)(4) + 4^{2} = x^{2} - 8x + 16$.

Add exponents on matching variables: $a^{3+(-1)} b^{-4+2} = a^2 b^{-2}\textsf{.}$

Combine $x^2$ terms: $x^2 + 2x^2 = 3x^2\textsf{.}$ The $x$ terms cancel: $4x - 4x = 0\textsf{.}$ Combine constants: $-5 + 9 = 4\textsf{.}$ Result: $3x^2 + 4\textsf{.}$

Expand: $(x - 1)(x - 6) = x^2 - 6x - x + 6 = x^2 - 7x + 6$.

$(2x + 1)^{2} = (2x)^{2} + 2(2x)(1) + 1^{2} = 4x^{2} + 4x + 1$.