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Question 512 Marks

Using the formula for squaring a binomial, evaluate the following:
$ (82)^2$

Answer

$(82)^2$
$=(80+2)^2$
$=(80)^2+2 \times 80 \times 2+(2)^2$
$=6400+320+4$
$=6724$

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Question 522 Marks

Using the formula for squaring a binomial, evaluate the following: $(69)^2$

Answer

$(69)^2$
$=(70-1)^2$
$=(70)^2-2 \times 70 \times 1+(1)^2$
$=4900-140+1$
$=4901-140$
$=4761$

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Question 532 Marks

Using the formula for squaring a binomial, evaluate the following:
$(103)^2$

Answer

$(103)^2$
$=(100+3)^2$
$=(100)^2+2 \times 100 \times 3+(3)^2$
$=10000+600+9$
$=10609$

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Question 542 Marks

Find the following products:
$ \left(x^2-a^2\right) \times (x-a) $

Answer

$ \left(x^2-a^2\right) \times (x-a) $
$ =x^2(x-a)-a^2(x-a) $
$ =x^3-a x^2-a^2 x+a^3 $

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Question 552 Marks

Find the value of: $\frac{198\times198-102\times102}{96}$

Answer

$\frac{198\times198-102\times102}{96}$ $=\frac{(198)^2-(102)^2}{96}$ $=\frac{(198-102)(198+102)}{96}$ $=\frac{300\times96}{96}$ $=300$

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Question 562 Marks

Find following products: $\Big(\text{x}+\frac{1}{\text{x}}\Big)\Big(\text{x}-\frac{1}{\text{x}}\Big)$

Answer

$\Big(\text{x}+\frac{1}{\text{x}}\Big)\Big(\text{x}-\frac{1}{\text{x}}\Big)$$=(\text{x})^2-\Big(\frac{1}{\text{x}}\Big)^2$
$\text{x}^2-\frac{1}{\text{x}^2}$

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Question 572 Marks

Find following products:
$ (4 x+5 y)(4 x+5 y) $

Answer

$ (4 x+5 y)(4 x+5 y) $
$ =(4 x+5 y)^2 $
$ =(4 x)^2+2 \times 4 x \times 5 y+(5 y)^2 $
$ =16 x^2+25 y^2+40 x y $

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Question 582 Marks

Expand: $(8a + 3b)^2$

Answer

$(8a + 3b)^2$
$= (8a)^2+ 2 × 8a × 3b + (3b)^2$
$= 64a^2+ 48ab + 9b^2$

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Question 592 Marks

Divide:
$12 x^4+8 x^3-6 x^2$ by $-2 x^2$

Answer

$\Big(12\text{x}^4 + 8\text{x}^3 - 6\text{x}^2 \Big)\div -2\text{x}^2$
$\Rightarrow\frac{12\text{x}^4}{ -2\text{x}^2}+\frac{8\text{x}^3}{-\text{2x}^2}-\frac{6\text{x}^2}{-2\text{x}^2}$
$\Rightarrow−6\text{x} $

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Question 602 Marks

Expand: $\Big(3\text{m}-\frac{4}{5}\text{n}\Big)^2$

Answer

$\Big(3\text{m}-\frac{4}{5}\text{n}\Big)^2$ $=\Big(\text{3m}\Big)^2-2\times3\text{m}\times\frac{4}{5}\text{n}+\Big(\frac{4}{5}\text{n}\Big)^2$ $=9\text{m}^2-\frac{24\text{mn}}{5}+\frac{16}{25}\text{n}^2$

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Question 612 Marks

Divide
$8 x^2 y^2-6 x y^2+10 x^2 y^3$ by $2 x y$

Answer

$(8\text{x}^2\text{y}^2 − 6\text{xy}^2 + 10\text{x}^2\text{y}^3 )\div 2\text{xy}$
$\Rightarrow\frac{8\text{x}^2\text{y}^2}{2\text{xy}}− \frac{6\text{xy}^2}{2\text{xy}}+ \frac{10\text{x}^2\text{y}^3}{ 2\text{xy }}$
$\Rightarrow4\text{xy} - 3\text{y} + 5\text{xy}^2$

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Question 622 Marks

Find following products:
$ \left(x^2+7\right)\left(x^2+7\right) $

Answer

$ \left(x^2+7\right)\left(x^2+7\right) $
$=\left(x^2+7\right)^2 $
$=\left(x^2\right)^2+7^2+2 \times x^2 \times 7 $
$ =x^4+49+14 x^2 $

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Question 632 Marks

Subtract: $2a - 5b + 2c - 9$ from $3a - 4b - c + 6$

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Question 642 Marks

Find the following products:
$\left(x^2-5 x+8\right) \times\left(x^2+2\right)$

Answer

$\left(x^2-5 x+8\right) \times\left(x^2+2\right)$
$=\left(x^2-5 x+8\right) \times x^2+\left(x^2-5 x+8\right) \times 2$
$=x^4-5 x^3+8 x^2+2 x^2-10 x+16$
$=x^4-5 x^3+10 x^2-10 x+16$

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Question 652 Marks

Add: $7x, -3x, 5x, -x, -2x$

Answer

$7x + (-3x) + 5x + (-x) + (-2x) $
$= 7x - 3x + 5x - x - 2x $
$= 12x - 6x $
$= 6x$

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Question 662 Marks

Find the following products:
$\left(3 x^2+5 x-9\right) \times(3 x-5)$

Answer

$\left(3 x^2+5 x-9\right) \times(3 x-5)$
$=3 x^2(3 x-5 x)+5 x(3 x-5)-9(3 x-5)$
$=9 x^3+15 x^2-27 x-15 x^2-25 x+45$
$=9 x^3-52 x+45$

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Question 672 Marks