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- Exercise 6.3
- e root of the following expressions.\\ (i) $4x^2-12xy +9y^2$\\ (ii) $x^2-1+\frac{1}{4x^2}, (x\neq 0)$\\ (iii) $\frac{1}{16}x^2-\frac{1}{12}xy+ \frac{1}{36}y^2$\\ (iv) $4(a+b)^2-12(a^2-b^2)+9(a-b)^2$\\ (v) $\frac{4x^6-12x^3y^3+9y^6}{9x^4-24x^2y^2+16y^4},(x \neq 0)$\\ (vi) $\left(
- Exercise 2.6 (Solutions) @matric:9th_science:unit_02
- \begin{array}{cl} 2(5+4i)-3(7+4i) &= 10+8i-21-12i\\ &= 10-21+8i-12i\\ &= -11-4i \end{array}$$ (iii) $$\begin{array}{cl} -(-3+5i)-(4+9i) ... 9i-6i^2\\ &= 6-5i-6(-1)\\ &= 6+6-5i\\ &= 12-5i \end{array}$$ ====Question 4==== * Simplify ... c{2(4+i)+3i(4+i)}{(4-i)(4+i)}\\ &= \frac{8+2i+12i+3i^2}{16-i^2}\\ &= \frac{8+14i-3}{16+1}\\
- Exercise 6.1
- sions by factorization.\\ (i) $x^2+5x+6$, $x^2-4x-12$ \\ (ii) $x^3-27$, $x^2+6x-27$, $2x^2-18$ \\ (iii... &=(x+3)(x+2) \end{align}$ $\begin{align} x^2-4x-12&=x^2-6x+2x-12,\\ &=x(x-6)+2(x-6)\\ &=(x-6)(x+2) \end{align}$ H.C.F= $x+2$ (ii) $\begin{align} x^3... &= 2 \times 2 \times 3 (x+1)(x-1)(x-1)(x^2+1)\\ &=12 (x^4-1)(x-1)\end{align}$ ====Question 6==== For
- Review exercise
- e H.C.F. of the following by factorization. $8x^4-128$ , $12x^3-96$\\ **Solution:**\\ $\begin{align}8x^4-128 &= 8(x^4-16)\\&=8[(x^2)^2-(4)^2]\\&= 2 \times 2\... (x^2+4)(x-2)(x+2)\end{align}$\\ $\begin{align}12 x^3-96&=12(x^3-8)\\&=2 \times 2\times 3 \times (x
- Exercise 6.2
- == $\frac{x^2-x-6}{x^2-9}+\frac{x^2+2x-24}{x^2-x-12}$\\ **Solution:**\\ $\begin{align} \frac{x^2-x-6}{x^2-9}&+\frac{x^2+2x-24}{x^2-x-12}\\ &=\frac{x^2-3x+2x-6}{(x)^2-(3)^2}+\frac{x^2+6x-4x-24}{x^2-4x+3x-12}\\&= \frac{x(x-3)+2(x-3)}{(x-3)(x+3)}+\frac{x(x+6... 4-1}\\&=4x\left(\frac{2+1}{x^4-1}\right)\\&=\frac{12x}{x^4-1}\end{align}$\\ ====Question 3:==== $\fr
- Exercise 4.1
- al expressions to the lowest forms.\\ (i) $\frac{120 x^2y^3z^5}{30x^3yz^2}$\\ (ii) $\frac{8a(x+1)}{2... ^2-4)^2}{4+3x-x^2}$\\ **Solution:**\\ (i) $\frac{120 x^2y^3z^5}{30x^3yz^2}$\\ $\begin{align}\frac{30\
- Exercise 2.3 (Solutions) @matric:9th_science:unit_02
- e following radical expression * (i) $\sqrt[3]{-125}$ * (ii) $\sqrt[4]{32}$ * (iii) $\sqrt[5]{\f... luton**\\ (i) $$\begin{array}{cl} \sqrt[3]{-125} &= \sqrt[3]{-5^3}\\ & = {-5}^{3\times\frac{1}{3
- Exercise 2.4 (Solutions) @matric:9th_science:unit_02
- ft(-3\right)}}\\ &=\frac{y^{-6}}{x^{-18} z^{-12}}\\ &=\frac{x^{18} z^{12}}{y^6} \end{array}$$ (iv) $$\begin{array}{cl} \frac{\left(81\right)^n.
- Exercise 2.5 (Solutions) @matric:9th_science:unit_02
- (ii) $i^{50}$ (iii) $i^{12}$ ... &= -1 \end{array}$$ (iii) $$\begin{array}{cl} i^{12} &= (i^2 )^6\\ &= {-1}^6\\ &= 1 \en
- Exercise 2.1 (Solutions) @matric:9th_science:unit_02
- ation**\\ * (i) o.68 * (ii) 4.75 * (iii) 7.125 * (iv) 11.3889 * (v) 0.625 * (vi) .65789