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Bug Institute: 3-LS1-1, 4-LS1-2
Energy Sources and the Environment: 4-ESS3-1, 5-ESS3-1
Examining Matter: 5-PS1-3, 5-PS1-4
Objects Attracted by Magnets: 3-PS2-3, 5-PS2-1
Rock Layers: 3-LS4-1, 4-ESS1-1
School Garden: 5-LS1-1, 5-LS2-1
Simple Cardboard Invention May Help Billions: 4-ESS3-1, 5-ESS3-1
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Icon for an open folder. Grouped by Topic.
Asteroid Belt: MS-PS2-1, MS-PS2-4
Cells Under a Microscope: MS-LS1-1, MS-LS1-3
Coral Reefs: MS-LS3-2, MS-LS4-4
Effect of Temperature on Water and Table Sugar: MS-PS1-1, MS-PS1-4
Groundwater: MS-ESS2-4, MS-ESS3-1
Maglev Trains: MS-PS2-3, MS-PS2-5
Moon Phase Activity: MS-ESS1-1, MS-ESS1-2, MS-ESS1-3
Observations of Plate Motion: MS-ESS1-4, MS-ESS2-2, MS-ESS2-3
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2025 Released Operational Items
Content CRs with Student Responses & Annotations
All MCAP Algebra I 2024 Released Items
Arithmetic with Polynomials and Rational Expressions (Algebra I)
Creating Equations (Algebra I)
Functions - Building Functions (Algebra I)
Functions - Interpreting Functions (Algebra I)
Functions - Linear, Quadratic, and Exponential Models (Algebra I)
Reasoning with Equations and Inequalities (Algebra I)
Seeing Structure in Expressions (Algebra I)
All MCAP Algebra II 2024 Released Items
Arithmetic with Polynomials & Rational Expressions (Algebra II)
Building Functions (Algebra II)
Interpreting Categorical and Quantitative Data (Algebra II)
Interpreting Functions (Algebra II)
Linear, Quadratic, & Exponential Models (Algebra II)
Reasoning with Equations and Inequalities (Algebra II)
Seeing Structure in Expressions (Algebra II)
The Complex Number System (Algebra II)
Icon for an open folder. Grouped by Standard.
Icon for an open folder. Grouped by Topic.
Arctic Ice: HS-ESS2-2, HS-ESS3-5
Calvert Cliffs: HS-LS4-1, HS-ESS2-7
Earthquake Energy: HS-PS4-1, HS-ESS2-2
Fukushima Butterflies: HS-LS1-1, HS-LS3-2
Global Cooling: HS-ESS2-4, HS-PS3-3
Honeybees and Almond Trees: HS-LS2-2, HS-LS2-6
Ladybird Beetle: HS-LS4-2, HS-LS4-5
Correct Answer
Choice B 24 plus 10 i \( (24 + 10 i) \) should be selected.
Explanation
To simplify open parenthesis 5 plus i close parenthesis squared, \( (5 + i)^2, \) we can expand the square using the distributive property (or the FOIL method) and then simplify.open parenthesis 5 plus i close parenthesis, squared, equals open parenthesis 5 plus i close parenthesis open parenthesis 5 plus i close parenthesis.
$$ (5 + i)^2 = (5 + i)(5 + i) $$
equals 25 plus 5 times i plus i times 5 plus i times i$$ = 25 + 5 \cdot i + i \cdot 5 + i \cdot i $$
equals 25 plus 5 i plus 5 i plus i squared$$ = 25 + 5i + 5i + i^2 $$
equals 25 plus 10 i plus i squared$$ = 25 + 10i + i^2 $$
We know that i squared equals negative 1, \( i^2 = -1, \) so substitute negative 1 \( -1 \) for i squared \( i^2: \) equals 25 plus 10 i plus open parenthesis negative 1, which equals 25 plus 10 i minus 1.
$$ = 25 + 10i + (-1) = 25 + 10i - 1 $$
equals 24 plus 10 i$$ = 24 + 10i $$
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