Digital SAT Math : Equivalent expressions -Practice Questions - New Syllabus
DSAT MAth Practice questions – all topics
- Advanced Math Weightage: 35% Questions: 13-15
- Equivalent expressions
- Nonlinear equations in one variable and systems of equations in two variables
- Nonlinear functions
DSAT MAth and English – full syllabus practice tests
▶️ Answer/Explanation
Ans: D
Expression: \( 256w^2 – 676 \).
Rewrite as difference of squares: \( (16w)^2 – 26^2 \).
Factor: \( (16w – 26)(16w + 26) \).
Choice A: Incorrect, expands to \( 256w^2 – 832w + 676 \).
Choice B: Incorrect, expands to \( 64w^2 – 169 \).
Choice C: Incorrect, expands to \( 64w^2 – 208w + 169 \).
▶️ Answer/Explanation
Ans: D
Simplify: \( 2 – x^{2} – x^{2} – 2 \).
Combine like terms: \( (2 – 2) + (-x^{2} – x^{2}) = 0 – 2x^{2} = -2x^{2} \).
Equivalent expression: \( -2x^{2} \).
Questions Easy
Which of the following expressions is equivalent to the sum of \((r^3+5r^2+7)\) and \((r^2+8r+12)\)?
A. \(r^5+13r^3+19\)
B.\(2r^3 +13r^2+19\)
C.\(r^3+5r^2+7r+12\)
D.\(r^3+6r^2+8r+19\)
▶️ Answer/Explanation
Ans: D
Sum: \( (r^3 + 5r^2 + 7) + (r^2 + 8r + 12) \).
Combine like terms:
\( r^3 \)-terms: \( r^3 \).
\( r^2 \)-terms: \( 5r^2 + r^2 = 6r^2 \).
\( r \)-terms: \( 8r \).
Constants: \( 7 + 12 = 19 \).
Result: \( r^3 + 6r^2 + 8r + 19 \).