Algebraic Expressions and Simplification - GRE Quantitative Reasoning
Card 1 of 22
What is the simplified form of $x^0$ for $x\ne 0$?
What is the simplified form of $x^0$ for $x\ne 0$?
Tap to reveal answer
$1$. Any non-zero number raised to the power of 0 equals 1 by definition.
$1$. Any non-zero number raised to the power of 0 equals 1 by definition.
← Didn't Know|Knew It →
What property justifies rewriting $a(b+c)$ as $ab+ac$?
What property justifies rewriting $a(b+c)$ as $ab+ac$?
Tap to reveal answer
Distributive property. The distributive property states that multiplication distributes over addition, allowing $a(b+c)$ to expand to $ab + ac$.
Distributive property. The distributive property states that multiplication distributes over addition, allowing $a(b+c)$ to expand to $ab + ac$.
← Didn't Know|Knew It →
What property justifies rewriting $ab+ac$ as $a(b+c)$?
What property justifies rewriting $ab+ac$ as $a(b+c)$?
Tap to reveal answer
Factoring using the distributive property. Factoring reverses the distributive property by extracting the common factor $a$ from $ab + ac$ to form $a(b + c)$.
Factoring using the distributive property. Factoring reverses the distributive property by extracting the common factor $a$ from $ab + ac$ to form $a(b + c)$.
← Didn't Know|Knew It →
What is the simplified form of $3x+5x$?
What is the simplified form of $3x+5x$?
Tap to reveal answer
$8x$. Combine like terms by adding the coefficients of $x$, resulting in $3 + 5 = 8$.
$8x$. Combine like terms by adding the coefficients of $x$, resulting in $3 + 5 = 8$.
← Didn't Know|Knew It →
What is the simplified form of $7a-2a+9a$?
What is the simplified form of $7a-2a+9a$?
Tap to reveal answer
$14a$. Combine like terms by computing the net coefficient: $7 - 2 + 9 = 14$.
$14a$. Combine like terms by computing the net coefficient: $7 - 2 + 9 = 14$.
← Didn't Know|Knew It →
What is the simplified form of $4(x-3)+2x$?
What is the simplified form of $4(x-3)+2x$?
Tap to reveal answer
$6x-12$. Distribute the 4 and combine like terms: $4x - 12 + 2x = 6x - 12$.
$6x-12$. Distribute the 4 and combine like terms: $4x - 12 + 2x = 6x - 12$.
← Didn't Know|Knew It →
What is the simplified form of $-(x-6)+2(x+1)$?
What is the simplified form of $-(x-6)+2(x+1)$?
Tap to reveal answer
$x+8$. Distribute the negative and the 2, then combine like terms: $-x + 6 + 2x + 2 = x + 8$.
$x+8$. Distribute the negative and the 2, then combine like terms: $-x + 6 + 2x + 2 = x + 8$.
← Didn't Know|Knew It →
What is the simplified form of $ rac{x^5}{x^2}$ for $x\ne 0$?
What is the simplified form of $ rac{x^5}{x^2}$ for $x\ne 0$?
Tap to reveal answer
$x^3$. Divide powers with the same base by subtracting exponents: $5 - 2 = 3$.
$x^3$. Divide powers with the same base by subtracting exponents: $5 - 2 = 3$.
← Didn't Know|Knew It →
What is the simplified form of $ rac{6a^3b^2}{2ab^5}$ using only positive exponents?
What is the simplified form of $ rac{6a^3b^2}{2ab^5}$ using only positive exponents?
Tap to reveal answer
$ rac{3a^2}{b^3}$. Convert negative exponent to positive by moving $b^{-3}$ to the denominator as $b^3$.
$ rac{3a^2}{b^3}$. Convert negative exponent to positive by moving $b^{-3}$ to the denominator as $b^3$.
← Didn't Know|Knew It →
What is the simplified form of $(x^3)^2$?
What is the simplified form of $(x^3)^2$?
Tap to reveal answer
$x^6$. Raise a power to a power by multiplying exponents: $3 cdot 2 = 6$.
$x^6$. Raise a power to a power by multiplying exponents: $3 cdot 2 = 6$.
← Didn't Know|Knew It →
What is the simplified form of $(2x^2y)^3$?
What is the simplified form of $(2x^2y)^3$?
Tap to reveal answer
$8x^6y^3$. Distribute the exponent to each factor: $2^3=8$, $(x^2)^3=x^6$, $y^3=y^3$.
$8x^6y^3$. Distribute the exponent to each factor: $2^3=8$, $(x^2)^3=x^6$, $y^3=y^3$.
← Didn't Know|Knew It →
What is the simplified form of $(x^{-2})(x^5)$ for $x\ne 0$?
What is the simplified form of $(x^{-2})(x^5)$ for $x\ne 0$?
Tap to reveal answer
$x^3$. Multiply powers with the same base by adding exponents: $-2 + 5 = 3$.
$x^3$. Multiply powers with the same base by adding exponents: $-2 + 5 = 3$.
← Didn't Know|Knew It →
What is the simplified form of $x^{-3}$ using only positive exponents?
What is the simplified form of $x^{-3}$ using only positive exponents?
Tap to reveal answer
$ rac{1}{x^3}$. A negative exponent indicates a reciprocal with the exponent made positive.
$ rac{1}{x^3}$. A negative exponent indicates a reciprocal with the exponent made positive.
← Didn't Know|Knew It →
What is the simplified form of $ rac{1}{x^{-2}}$ for $x\ne 0$?
What is the simplified form of $ rac{1}{x^{-2}}$ for $x\ne 0$?
Tap to reveal answer
$x^2$. The reciprocal of a negative exponent simplifies to the base with a positive exponent: $x^{-(-2)} = x^2$.
$x^2$. The reciprocal of a negative exponent simplifies to the base with a positive exponent: $x^{-(-2)} = x^2$.
← Didn't Know|Knew It →
What is the simplified form of $ rac{2}{3}x+ rac{1}{6}x$?
What is the simplified form of $ rac{2}{3}x+ rac{1}{6}x$?
Tap to reveal answer
$ rac{5}{6}x$. Add fractions with common denominator 6: $ rac{4}{6}x + rac{1}{6}x = rac{5}{6}x$.
$ rac{5}{6}x$. Add fractions with common denominator 6: $ rac{4}{6}x + rac{1}{6}x = rac{5}{6}x$.
← Didn't Know|Knew It →
What is the simplified form of $ rac{3x}{4}- rac{x}{8}$?
What is the simplified form of $ rac{3x}{4}- rac{x}{8}$?
Tap to reveal answer
$ rac{5x}{8}$. Subtract fractions with common denominator 8: $ rac{6x}{8} - rac{x}{8} = rac{5x}{8}$.
$ rac{5x}{8}$. Subtract fractions with common denominator 8: $ rac{6x}{8} - rac{x}{8} = rac{5x}{8}$.
← Didn't Know|Knew It →
What is the simplified form of $ rac{x^2-9}{x-3}$ for $x\ne 3$?
What is the simplified form of $ rac{x^2-9}{x-3}$ for $x\ne 3$?
Tap to reveal answer
$x+3$. Factor numerator as $(x-3)(x+3)$ and cancel common factor $(x-3)$ with denominator.
$x+3$. Factor numerator as $(x-3)(x+3)$ and cancel common factor $(x-3)$ with denominator.
← Didn't Know|Knew It →
What is the simplified form of $ rac{x^2+5x}{x}$ for $x\ne 0$?
What is the simplified form of $ rac{x^2+5x}{x}$ for $x\ne 0$?
Tap to reveal answer
$x+5$. Factor $x$ from numerator and cancel with denominator: $ rac{x(x+5)}{x} = x+5$.
$x+5$. Factor $x$ from numerator and cancel with denominator: $ rac{x(x+5)}{x} = x+5$.
← Didn't Know|Knew It →
What is the simplified form of $ rac{x^2-4}{x^2+4x+4}$ for $x\ne -2$?
What is the simplified form of $ rac{x^2-4}{x^2+4x+4}$ for $x\ne -2$?
Tap to reveal answer
$ rac{x-2}{x+2}$. Factor numerator as $(x-2)(x+2)$ and denominator as $(x+2)^2$, then cancel one $(x+2)$.
$ rac{x-2}{x+2}$. Factor numerator as $(x-2)(x+2)$ and denominator as $(x+2)^2$, then cancel one $(x+2)$.
← Didn't Know|Knew It →
What is the simplified form of $(x+3)^2$?
What is the simplified form of $(x+3)^2$?
Tap to reveal answer
$x^2+6x+9$. Expand using FOIL or square binomial formula: $x^2 + 2cdot xcdot 3 + 3^2$.
$x^2+6x+9$. Expand using FOIL or square binomial formula: $x^2 + 2cdot xcdot 3 + 3^2$.
← Didn't Know|Knew It →
What is the simplified form of $(x-5)(x+5)$?
What is the simplified form of $(x-5)(x+5)$?
Tap to reveal answer
$x^2-25$. Apply difference of squares formula: $x^2 - 5^2$.
$x^2-25$. Apply difference of squares formula: $x^2 - 5^2$.
← Didn't Know|Knew It →
What is the simplified form of $x^2-10x+25$?
What is the simplified form of $x^2-10x+25$?
Tap to reveal answer
$(x-5)^2$. Factor as perfect square trinomial: coefficients fit $(x-5)^2 = x^2 - 10x + 25$.
$(x-5)^2$. Factor as perfect square trinomial: coefficients fit $(x-5)^2 = x^2 - 10x + 25$.
← Didn't Know|Knew It →