The image provided is a reference sheet containing standard mathematical formulas. It does not contain a specific question or problem to solve. Therefore, there is no single "answer" to provide.
However, I can summarize the key formulas presented in the sheet for your reference:
1. Algebra Formulas
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Square of a sum: $(a + b)^2 = a^2 + 2ab + b^2$
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Square of a difference: $(a - b)^2 = a^2 - 2ab + b^2$
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Difference of squares: $a^2 - b^2 = (a - b)(a + b)$
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Cube of a sum: $(a + b)^3 = a^3 + b^3 + 3ab(a + b)$
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Cube of a difference: $(a - b)^3 = a^3 - b^3 - 3ab(a - b)$
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Sum of cubes: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$
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Difference of cubes: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$
2. Distance Between Two Points
To find the distance between point $(x_1, y_1)$ and point $(x_2, y_2)$:
$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$
3. Trigonometry (Right-Angled Triangle)
For an angle $\theta$:
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Sine: $\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}$
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Cosine: $\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}$
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Tangent: $\tan \theta = \frac{\text{Opposite}}{\text{Adjacent}}$
4. Pythagoras Theorem
In a right-angled triangle with legs $a$ and $b$ and hypotenuse $c$:
$$ a^2 + b^2 = c^2 $$
Final Answer:
The image is a formula reference sheet and does not contain a specific problem to solve. Please provide a specific question if you need help with a calculation using these formulas.
Parent Tip: Review the logic above to help your child master the concept of 7th grade formulas.
