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- Exercise 6.1
- 3-2x^2)$, $54(27x^4-x)$ **Solution:**\\ (i) $\begin{align} x^2+5x+6&=x^2+3x+2x+6,\\ &=x(x+3)+2(x+3)\\ &=(x+3)(x+2) \end{align}$ $\begin{align} x^2-4x-12&=x^2-6x+2x-12,\\ &=x(x-6)+2(x-6)... &=(x-6)(x+2) \end{align}$ H.C.F= $x+2$ (ii) $\begin{align} x^3-27 &=x^3-3^3,\\ &=(x-3)(x^2+3x+9)\end{align}$ $\begin{align} x^2+6x-27&=x^2+9x-3x-27,\\ &=x(x+9)-3(x+9)
- Exercise 2.6 (Solutions) @matric:9th_science:unit_02
- +3i^{16}-6i^{19}+4i^{25}$ **Solution**\\ (i) $$\begin{array}{cl} (2+3i)+(7-2i) &= 2+3i+7-2i\\ &= 2+7+3i-2i\\ &= 9+i \end{array}$$ (ii) $$\begin{array}{cl} 2(5+4i)-3(7+4i) &= 10+8i-21-12i\\ ... 21+8i-12i\\ &= -11-4i \end{array}$$ (iii) $$\begin{array}{cl} -(-3+5i)-(4+9i) &= 3-5i-4-9i\\ ... 3-4-5i-9i\\ &= -1-14i \end{array}$$ (iv) $$\begin{array}{cl} 2i^2+6i^3+3i^{16}-6i^{19}+4i^{25}
- Exercise 6.3
- (i) $4x^2-12xy +9y^2$\\ **Solution:**\\ $\begin{align}4x^2-12xy +9y^2\\&=4x^2-6xy-6xy +9y^2\\&= 2... &= (2x-3y)(2x-3y)\\&= (2x-3y)^2 \end{align}$\\ $\begin{align} \sqrt{4x^2-12xy +9y^2}&= \pm (2x-3y) \end{... frac{1}{4x^2}, (x\neq 0)$\\ **Solution:**\\ $\begin{align}x^2-1+\frac{1}{4x^2}\\&=(x)^2-1+(\frac{1}{2... x})^2\\&= (x-\frac{1}{2x})^2 \end{align}$\\ $\begin{align} \sqrt{x^2-1+\frac{1}{4x^2}}&= \pm (x-\frac
- Exercise 2.5 (Solutions) @matric:9th_science:unit_02
- (vi) $i^{27}$ **Solution**\\ (i) $$\begin{array}{cl} i^7 &= {i^6}\cdot i\\ &= (i^2)^3\cd... {-1}^3 \cdot i\\ &= -i \end{array}$$ (ii) $$\begin{array}{cl} i^{50} &= (i^2 )^{25}\\ &= {-1}^{25}\\ &= -1 \end{array}$$ (iii) $$\begin{array}{cl} i^{12} &= (i^2 )^6\\ &= {-1}^6\\ &= 1 \end{array}$$ (iv) $$\begin{array}{cl} (-i)^8 &= (-i^2 )^4\\ &= {-1}^4
- Review exercise
- $8x^4-128$ , $12x^3-96$\\ **Solution:**\\ $\begin{align}8x^4-128 &= 8(x^4-16)\\&=8[(x^2)^2-(4)^2]\\... es 2 \times (x^2+4)(x-2)(x+2)\end{align}$\\ $\begin{align}12 x^3-96&=12(x^3-8)\\&=2 \times 2\times 3 \times (x-2)(x^2+ 2 x+4)\end{align}$\\ $\begin{align} H.C.F. &= 2 \times 2 (x-2)\\&= 4(x-2)\end... 6x^2-13x-5, 4x^2-20x+25$\\ **Solution:**\\ $\begin{align}12x^2-75 &= 3(4x^2-25)\\&=3[(2x)^2-(5)^2]\\
- Exercise 6.2
- rac{x^2+2x-24}{x^2-x-12}$\\ **Solution:**\\ $\begin{align} \frac{x^2-x-6}{x^2-9}&+\frac{x^2+2x-24}{x^... \right]+\frac{4x}{x^4-1}$\\ **Solution:**\\ $\begin{align} \left[\frac{x+1}{x-1}-\frac{x-1}{x+1}-\fra... 4x+3}-\frac{2}{x^2-6x+5}$\\ **Solution:**\\ $\begin{align} \frac{1}{x^2-8x+15}+\frac{1}{x^2-4x+3}-\fr... 4x+3}-\frac{2}{x^2-6x+5}$\\ **Solution:**\\ $\begin{align} \frac{1}{x^2-8x+15}+\frac{1}{x^2-4x+3}-\fr
- Exercise 2.4 (Solutions) @matric:9th_science:unit_02
- right)\left(3^3\right)}$ **Solution**\\ (i) $$\begin{array}{cl} \begin{array}{cl} \frac{(243)^{\frac{-2}{3}}(32)^{\frac{-1}{5}}}{\sqrt(196)^{-1}} &= \frac... .\sqrt[3]{3}} \end{array}\end{array}$$ (ii) $$\begin{array}{cl} \left(2x^5y^{-4}\right)\left(-8x^{-3}y... &= \frac{-16x^2}{y^2} \end{array}$$ (iii) $$\begin{array}{cl} \left(\frac{x^{-2}y^{-1}z^{-4}}{x^4y^{
- Exercise 4.1
- on:**\\ (i) $\frac{120 x^2y^3z^5}{30x^3yz^2}$\\ $\begin{align}\frac{30\times 4 y^(3-1)z^(5-2)}{30x^(3-2)}... olution:**\\ (ii) $\frac{8 a(x+1)}{2(x^2-1)}$\\ $\begin{align}\frac{2\times 4a(x+1)}{2(x+1)(x-1)}\\&= \fr... tion:**\\ (iii) $\frac{(x+y)^2-4xy}{(x-y)^2}$\\ $\begin{align}\frac{x^2+y^2+2xy-4xy}{x^2-2xy+y^2}\\&= 1\e... c{(x^3-y^3)(x^2-2xy+y^2)}{(x-y)(x^2+xy+y^2)}$\\ $\begin{align}\frac{(x^3-y^3)(x^2-2xy+y^2)}{(x^3-y^3)}\\&
- Exercise 11.1 (Solutions) @matric:9th_science:unit11
- $m\angle B=m\angle D=130^\circ$ We know that\\ \begin{align} & m\angle A +\,\,m\angle B=180^\circ \\ &... , $m\angle DAB=?$, $m\angle C=?$, $m\angle D=?$ \begin{align} & m\angle DAM+m\angle DAB=180^\circ \\ & 4... circ \\ & m\angle DAB=140^\circ \end{align} Also \begin{align} & m\angle DAB+m\angle B=180^\circ \\ & 140... 0^\circ \\ & m\angle B=40^\circ \end{align} Now \begin{align} & m\angle B =m\angle D=40^\circ \\ \Righta
- Exercise 2.3 (Solutions) @matric:9th_science:unit_02
- rt[3]{\frac{-8}{27}}$ **Soluton**\\ (i) $$\begin{array}{cl} \sqrt[3]{-125} &= \sqrt[3]{-5^3}\\ & =... es\frac{1}{3}}\\ &= {-5} \end{array}$$ (ii) $$\begin{array}{cl} \sqrt[4]{32} &= \sqrt[4]{{2}^5}\\ &= \... 4]{2}\\ &= 2\sqrt[4]{2} \end{array}$$ (iii) $$\begin{array}{cl} \sqrt[5]{\frac{3}{32}} &= \left(\frac{... end{array}$$ (iv) $$\begin{array}{cl} \sqrt[3]{\frac{-8}{27}} &= \sqrt[3]{\l
- Exercise 2.2 (Solutions) @matric:9th_science:unit_02
- ting the properties of the real numbers used, $$ \begin{array}{cl} 3x + 3(y - x) &= 3x + 3y - 3x ... ...