Find the square of:
(i) 2a+b
(ii) 3a+7b
(iii) 3a-4b
\text { (iv) } \frac{3 a}{2 b}-\frac{2 b}{3 a}
Use identities to evaluate:
(i) 101²
(ii) 502²
(iii) 97²
(iv) 998²
Evaluate:
\begin{aligned} &\text { (i) }\\ &\left(\frac{7}{8} x+\frac{4}{5} y\right)^{2} \end{aligned}
\begin{aligned} &(\mathrm{ii})\\ &\left(\frac{2 x}{7}-\frac{7 y}{4}\right)^{2} \end{aligned}
If a-b=7 and ab = 18; find a+b.
If ? +1/a= ? and ? ≠ 0; find:
(i) ? −1/a
(ii) ?² −1/a²
12.If a2-3a+1=0 and a≠0; find:
(i) ? + 1/a
\text { (ii) } \quad a^{2}+\frac{1}{a^{2}}
The number x is 2 more than the number y. If the sum of the squares of x and y is 34; find the product of x and y.
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Find the cube of:
(i) 3a-2b
(ii) 5a+3b
\text { (iii) } \quad 2 a+\frac{1}{2 a} ;(a \neq 0)
\text { (iv) } \quad 3 a-\frac{1}{a} ;(a \neq 0)
If a + 2b = 5; then show that: a^{3}+8 b^{3}+30 a b=125
\text { If } a \neq 0 \text { and } a-\frac{1}{a}=4 ; \text { find: }\text { (i) } a^{2}+\frac{1}{a^{2}}\text { (ii) } \quad a^{4}+\frac{1}{a^{4}}\text { (iii) } \quad a^{3}-\frac{1}{a^{3}}
\begin{aligned} &\text { If } x \neq 0 \text { and } x-\frac{1}{x}=2 ; \text { then show that: }\\ &x;^{2}+\frac{1}{x^{2}}=x^{3}+\frac{1}{x^{3}}=x^{4}+\frac{1}{x^{4}} \end{aligned}
If 2x-3y=10 and xy=16; find the value of 8x³-27y³ .
Two positive numbers x and y are such that x>y. if the difference of these numbers is 5 and their product is 24, find:
(i) Sum of these numbers.
(ii) Difference of their cubes.
(iii) Sum of their cubes.
\text { If } 4 x^{2}+y^{2}=a \text { and } x y=b, \text { find the value of } 2 x+y
Expand:\text { (i) }\left(2 x-\frac{1}{x}\right)\left(3 x+\frac{2}{x}\right)
\text { (ii) }\left(3 a+\frac{2}{b}\right)\left(2 a-\frac{3}{b}\right)
\text { If } a+b+c=12 \text { and } a^{2}+b^{2}+c^{2}=50 ; \text { find } a b+b c+c a
\text { If } a^{2}+b^{2}+c^{2}=35 \text { and } a b+b c+c a=23 ; \text { find } a+b+c
\text { If } a+b+c=p \text { and } a b+b c+c a=q ; \text { find } a^{2}+b^{2}+c^{2}
\begin{array}{l} \text { If } x+2 y+3 z=0 \text { and } \\ x^{3}+4 y^{3}+9 z^{3}=18 x y z ; \text { evaluate; } \\ \frac{(x+2 y)^{2}}{x y}+\frac{(2 y+3 z)^{2}}{y z}+\frac{(3 z+x)^{2}}{z x} \end{array}
\text { In the expansion of }\left(2 x^{2}-8\right)(x-4)^{2} ; \text { find the value of: }
(i) Coefficient of x³
(ii) Coefficient of x²
(iii) Constant term.
\text { If } x>0 \text { and } x^{2}+\frac{1}{9 x^{2}}=\frac{25}{36}, \text { find: } x^{3}+\frac{1}{27 x^{3}}
\text { If } 2\left(x^{2}+1\right)=5 x, \text { find: }\text { (i) } \quad x-\frac{1}{x}\text { (ii) } \quad x^{3}-\frac{1}{x^{3}}
\text { If } a^{2}+b^{2}=34 \text { and } a b=12 ; \text { find: }
(i)(a+b)^{2}+5(a-b)^{2}
(ii)(a+b)^{2}+5(a-b)^{2}
\begin{aligned} &\text { If } 3 x-\frac{4}{x}=4 \text { and } x \neq 0 ; \text { find: }\\ &27 x^{3}-\frac{64}{x^{3}} \end{aligned}
\text { If } \quad x=\frac{1}{5-x} \text { and } x \neq 5, \text { find: } x^{3}-\frac{1}{x^{3}}
The difference between two positive numbers is 4 and the difference between their cubes is 316. Find:
(i) their product
(ii) the sum of their squares.
Using suitable identity, evaluate:
(i) (104)³
(ii) (97)³
Evaluate: \text { (i) } \frac{0.8 \times 0.8 \times 0.8+0.5 \times 0.5 \times 0.5}{0.8 \times 0.8-0.8 \times 0.5+0.5 \times 0.5} \text { (ii) } \frac{1.2 \times 1.2+1.2 \times 0.3+0.3 \times 0.3}{1.2 \times 1.2 \times 1.2-0.3 \times 0.3 \times 0.3}
\text { If } x+5 y=10 ; \text { find the value of } x^{3}+125 y^{3}+150 x y-1000
\text { If } x=3+2 \sqrt{2}, \text { find: }\text { (i) } \frac{1}{x}\text { (ii) } x-\frac{1}{x}\text { (iii) }\left(x-\frac{1}{x}\right)^{3}\text { (iv) } x^{3}-\frac{1}{x^{3}}
Prove that: x^{2}+y^{2}+z^{2}-x y-y z-z x \text { is always positive. }
Find:
(i) (a + b)(a + b) = (a + b)²
(ii) (a + b)(a + b)(a + b)
(iii) (a – b)(a – b)(a – b) by using the result of part (ii)
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