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Michael O.

Tutor for 15 years

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Pre-Calculus

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Question:

Using the quadratic formula, solve this equation: $$x^{2}+3x-40=0$$

Michael O.

Answer:

The quadratic formula is: $$x = \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$$ In our question, $$a=1, b=3, c=-40$$ Putting these values into the quadratic formula yields: $$x=-8$$ or $$x= 5$$

Pre-Algebra

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Question:

Evaluate the following expression: $$(\frac{9}{16})^{\frac{3}{2}}$$

Michael O.

Answer:

Consider the fractional exponent: The denominator means a square root, while the numerator means a power of 3. We apply the denominator first: $$\sqrt{\frac{9}{16}}=\frac{3}{4}$$ Then apply the power of 3: $$(\frac{3}{4})^{3}= \frac{27}{64}$$ So, $$(\frac{9}{16})^{\frac{3}{2}}= \frac{27}{64}$$

Basic Math

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Question:

Factorise completely: $$18x^{2} - 50y^{2}$$

Michael O.

Answer:

$$18x^{2} - 50y^{2}$$ $$=2(9x^{2} - 25y^{2})$$ Using difference of squares, factorize the expression in the brackets $$=2(3x + 5y)(3x - 5y)$$

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