Basic algebra
Practice Questions
Simplify the expression: $$\frac{a^5 \times b^3 \times c^7}{a^4 \times b^8 \times c^9}$$...
#2Simplify the expression: $$(5z - 7y)^2 + (7z + 5y)^2 - 49z^2$$...
#3If $x = 4 + \sqrt{6}$ and $y = 4 - \sqrt{6}$, then find the value of $x^2 + y^2$....
#4Simplify the expression $$(5z - 12y)^2 + (12z + 5y)^2 - 144z^2$$...
#5Simplify the expression $$\frac{a^{7} \times b^{8} \times c^{7}}{a^{9} \times b^{5} \times c^{4}}$$....
#6If $x = 8 + \sqrt{5}$ and $y = 8 - \sqrt{5}$, then find the value of $x^2 + y^2$....
#7Find the value of *Y* from the system of equations: $$\begin{cases} X - 2Y + 2Z = 16 \\ X - Y + Z = 9 \\ 2X - 3Y - Z = ...
#8The second number in the given number-pairs is obtained by performing certain mathematical operation(s) on the first num...
#9If $x + \frac{1}{x} = 4$, find the value of $x^2 + \frac{1}{x^2}$....
#10For what value of *m* will the system of equations $$17x + my + 102 = 0$$ and $$23x + 299y + 138 = 0$$ have an infinite...
#11What is the simplified form of the expression $$ (1 + x)(1 + x^2)(1 + x^4)(1 + x^8)(1 - x) $$?...
#12Find the value of the infinite nested radical expression: $$ \sqrt{20 - \sqrt{20 - \sqrt{20 - \sqrt{20 - \ldots}}}} $$...
#13Find the **LCM** of the polynomials: $$x^2 - 8x + 15 \quad \text{and} \quad x^2 - 5x + 6$$...
#14If $4x^2 + y^2 = 40$ and $xy = 6$, then find the value of $2x + y$....
#15If the highest common factor (HCF) of *x* and *y* is 15, then the HCF of $$36x^2 - 81y^2$$ and $$81x^2 - 9y^2$$ is divis...
#16Evaluate the value of the expression: $$\frac{0.7^3 + 0.3^3}{0.7^2 - 0.7 \times 0.3 + 0.3^2}$$...
#17Solve the system of equations: $$ \begin{cases} 2^x + 3^y = 17 \\ 2^{x^2} - 3^{y+1} = 5 \end{cases} $$ Find the values...
#18If $$ A = \frac{58^2 - 25^2}{46^2 - 37^2} $$ and $$ B = \frac{26^2 - 15^2}{56^2 - 15^2}, $$ then find the value of $$ \f...
#19Find the value of $$\frac{\sqrt{1.24} \times \sqrt{2.79}}{\sqrt{2.64} \times \sqrt{5.94}}$$...
#20Simplify the expression: $$\frac{a^5 \times b^3 \times c^7}{a^4 \times b^8 \times c^9}$$...
#21Simplify the expression: $$(5z - 7y)^2 + (7z + 5y)^2 - 49z^2$$...
#22If $x = 4 + \sqrt{6}$ and $y = 4 - \sqrt{6}$, then find the value of $x^2 + y^2$....
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