Equivalent Expressions - SAT Math

$2x$. Distribute -2, then combine like terms.

$x + 6$. Distribute -3, then combine like terms.

$a \times 1 = a$. Multiplying by 1 doesn't change the value.

$5x - 3$. Distribute 3, then combine like terms.

$9x^2 - 12x + 4$. Expand using $(a - b)^2 = a^2 - 2ab + b^2$.

$5x - 3$. Distribute negative sign, then combine like terms.

$ab = ba$. Order doesn't matter in multiplication.

$6y - 12$. Distribute 4, then combine like terms.

$4a + 8$. Distribute 4 to both terms inside parentheses.

$a \times \frac{1}{a} = 1$ for $a \neq 0$. Multiplying by reciprocal gives 1.

$-x + 10$. Distribute 2, then combine like terms.

7x. Combine like terms by adding coefficients.

$-a + 8$. Distribute -4, then combine like terms.

$x^2 - 2x$. Distribute $x$, then combine like terms.

$a(b + c) = ab + ac$. Multiplying distributes over addition inside parentheses.

$2x + 6$. Distribute 3, then combine like terms.

$2x + 11$. Distribute 2, then add 3.

$7x - 5$. Distribute 5, then combine like terms.

$a + 0 = a$. Adding zero doesn't change the value.

$(a - b)^2$. Perfect square trinomial pattern: $a^2 - 2ab + b^2 = (a - b)^2$.

$(2x - 3)(2x + 3)$. Difference of squares: $(2x)^2 - 3^2 = (2x - 3)(2x + 3)$.

$-x + 10$. Distribute both terms, then combine like terms.

$5x$. Combine like terms by adding coefficients.

$5a + 5b$. Distribute 5 to both terms inside parentheses.

$7y + 4$. Group like terms and combine coefficients.

$7x^2$ and $-2x^2$. Like terms have the same variable and exponent.

$(x - 2)(x + 2)$. Difference of squares: $a^2 - b^2 = (a - b)(a + b)$.

$5x - 4$. Distribute and combine: $2x - 10 + 3x + 6 = 5x - 4$.

$5x + 12$. Distribute 3, then combine like terms.

$2x$. Add fractions with same denominator: $\frac{3x + x}{2} = \frac{4x}{2} = 2x$.

$a + 8$. Distribute 2, then combine like terms.

$(a + b) + c = a + (b + c)$. Grouping doesn't change the sum.

$11 - 2x$. Distribute negative sign, then combine like terms.

$11x - 8$. Distribute 2, then combine like terms.

$2x + 2$. Combine like terms by adding coefficients.

$(x + y)^2$. Perfect square trinomial pattern: $a^2 + 2ab + b^2 = (a + b)^2$.

$-2x + 6$. Distribute then combine like terms: $2x + 6 - 4x = -2x + 6$.

$4a + 8$. Distribute 4 to both terms inside parentheses.

$5x + 12$. Distribute 3, then combine like terms.

$5x - 3$. Distribute negative sign, then combine like terms.

$5x$. Combine like terms by adding coefficients.

$a \times 1 = a$. Multiplying by 1 doesn't change the value.

$6y - 12$. Distribute 4, then combine like terms.

$5x - 3$. Distribute 3, then combine like terms.

$7x - 5$. Distribute 5, then combine like terms.

$x + 6$. Distribute -3, then combine like terms.

$2x + 6$. Distribute 3, then combine like terms.

$a + 8$. Distribute 2, then combine like terms.

$2x + 11$. Distribute 2, then add 3.

$(a + b) + c = a + (b + c)$. Grouping doesn't change the sum.

$x + 4$. Distribute negative, then combine like terms.

$ab = ba$. Order doesn't matter in multiplication.

$11x - 8$. Distribute 2, then combine like terms.

$-x + 10$. Distribute both terms, then combine like terms.

$11 - 2x$. Distribute negative sign, then combine like terms.

$a(b + c) = ab + ac$. Multiplying distributes over addition inside parentheses.

$7x^2$ and $-2x^2$. Like terms have the same variable and exponent.

$7y + 4$. Group like terms and combine coefficients.

$2x$. Distribute -2, then combine like terms.

$-x + 10$. Distribute 2, then combine like terms.

$-a + 8$. Distribute -4, then combine like terms.

$x^2 - 2x$. Distribute $x$, then combine like terms.

$a + 0 = a$. Adding zero doesn't change the value.

$2x + 2$. Combine like terms by adding coefficients.

$a \times \frac{1}{a} = 1$ for $a \neq 0$. Multiplying by reciprocal gives 1.