Question : Simplify the following expression. $\{[(x-5)(x-1)]-[(9 x-5)(9x-1)]\} \div 16x$
Option 1: $2x(5x-3)$
Option 2: $-(5x-3)$
Option 3: $x(5x-3)$
Option 4: $-6x(5x-3)$
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Correct Answer: $-(5x-3)$
Solution : Given: $\{[(x-5)(x-1)]-[(9 x-5)(9x-1)]\} \div 16x$ $= [(x^{2}-x-5x+5)-[(81x^{2}-9x-45x+5)]\div 16x$ $= [(x^{2}-6x+5)-[(81x^{2}-54x+5)]\div 16x$ $= [(x^{2}-6x+5-81x^{2}+54x-5)]\div 16x$ $= [-80x^{2}+48x]\div 16x$ $=[-5x+3]$ $=-(5x-3)$ Hence, the correct answer is $-(5x-3)$.
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Question : The simplified form of $(x+3)^2+(x-1)^2$ is:
Option 1: $(x^2+2x+5)$
Option 2: $2(x^2+2x+5)$
Option 3: $(x^2-2x+5)$
Option 4: $2(x^2-2x+5)$
Question : The simplified form of $(x+3)^{2}+(x-1)^{2}$ is:
Option 1: $(x^{2}+2x+5)$
Option 2: $2(x^{2}+2x+5)$
Option 3: $(x^{2}-2x+5)$
Option 4: $2(x^{2}-2x+5)$
Question : Simplify the given expression $\frac{(x+3)^3+(x-3)^3}{x^2+27}$.
Option 1: $3x$
Option 2: $x$
Option 3: $4x$
Option 4: $2x$
Question : Expand and simplify $(x+4)^2+(x-2)^2$.
Option 1: $2(x^2+2x+10)$
Option 2: $2(x^2+2x-10)$
Option 3: $2(x^2-2x+10)$
Option 4: $2(x^2-2x-10)$
Question : Simplify the given expression and find the value for $x=-1$. $\frac{10 x^2+5 x+2 x y+y}{5 x+y}$
Option 1: –1
Option 2: 0
Option 3: 1
Option 4: 2
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