Question : If $a=17, b=13$, then find the value of the expression $\left(a^3-b^3 – 3a^2b+3ab^2\right)$.

Option 1: – 64

Option 2: – 27000

Option 3: 27000

Option 4: 64

Question : If $\frac{4\left[(17)^3-(7)^3\right]}{\left(17^2+7^2+p\right)}=40$, then what is the value of $p$?

Option 1: –119

Option 2: –129

Option 3: 119

Option 4: 129

Question : What is the value of (a + b)³ – a³ + b³?

Option 1: –3ab(a – b) + 2b³

Option 2: 3ab(a + b) + 2b³

Option 3: 3ab(a – b) + b³

Option 4: –3ab(a + b) + b³

Question : If $\small a^{4}+1=\left [\frac{a^{2}}{b^{2}}\right ]\left (4b^{2}-b^{4}-1\right),$ then what is the value of $a^{4}+b^{4}?$

Option 1: 2

Option 2: 16

Option 3: 32

Option 4: 64

Question : Find the value of the given expression.
3 – (– 6) {– 2 – 9 – 3} ÷ 7{1 + (– 2) (– 1)}

Option 1: –1

Option 2: 15

Option 3: 7

Option 4: 1

Question : Expand and simplify the algebraic expression:
$(x-5)^2+(x+3)^2+4x$

Option 1: $2\left(x^2-17\right)$

Option 2: $2\left(x^2+17\right)$

Option 3: $\left(x^2+17\right)$

Option 4: $2\left(x^2-5 x+17\right)$