Question 512 Marks
Subtract:
$x^3+3 x^2-5 x+4$ from $3 x^3-x^2+2 x-4$
View full question & answer→Question 522 Marks
Add $: 3a - 4b + 4c, 2a + 3b - 8c, a - 6b + c$
AnswerWriting the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:
$3 a-4 b+4 c$
$2 a+3 b-8 c$
$a-6 b+c$
$\overline{6 a-7 b-3} c$
View full question & answer→Question 532 Marks
Find the continues products:
$(x-3)(x+3)\left(x^2+9\right)$
Answer$(x-3)(x+3)\left(x^2+9\right)$
$=\left\{(x)^2-(3)^2\right\}\left(x^2+9\right)$
$=\left(x^2-9\right)\left(x^2+9\right)$
$=\left(x^2\right)^2-(9)^2$
$=x^4-81$
View full question & answer→Question 542 Marks
Subtract:
What must be subtracted from $3 a^2-6 a b-3 b^2-1$ to get $4 a^2-7 a b-4 b^2+1$ ?
View full question & answer→Question 552 Marks
Find the following products:
$\left(x^3-5 x^2+3 x+1\right) \times\left(x^3-3\right)$
Answer$\left(x^3-5 x^2+3 x+1\right) \times\left(x^3-3\right)$
$=x^2\left(x^3-5 x^2+3 x+1\right)-3\left(x^3-5 x^2+3 x+1\right)$
$=x^5-5 x^4+3 x^3+x^2-3 x^3+15 x^2-9 x-3$
$=x^5-5 x^4+16 x^2-9 x-3$
View full question & answer→Question 562 Marks
Find the value of expression $\left(36 x^2+25 y^2-60 x y\right)$, when $x =\frac{2}{3}$ and $y =\frac{1}{5}$.
Answer$(36\text{x}^2 + 25\text{y}^2 - 60\text{xy})$
$= (6\text{x})^2 + (5\text{y})^2 - 2 × 6\text{x} × 5\text{y}$
$= (6\text{x} - 5\text{y})^2$
$=\Big(6\times\frac{2}{3}-5\times\frac{1}{5}\Big)^2$
$=(4-1)^2$
$=(3)^2=9$
View full question & answer→Question 572 Marks
Write the quotient and remainder when we divide:
$\left(15 x^2+x-6\right)$ by $(3 x+2)$
View full question & answer→Question 582 Marks
The perimeter of a triangle is $6 p^2-4 p+9$ and two of its sides are $p^2-2 p+1$ and $3 p^2-5 p+3$. Find the third side of the triangle.
AnswerPerimeter of triangle $=6 p^2-4 p+9$
Sum of two sides of it $=3 p^2-5 p+3+p^2-2 p+1$
$=4 p^2-7 p-4$
$\text { Third side }=\left(6 p^2-4 p+9\right)-\left(4 p^2+7 p-4\right)$
$=6 p^2-4 p+9-4 p^2+7 p-4$
$=2 p^2+3 p+5$
View full question & answer→Question 592 Marks
Find the following products:
$\left(3 p^2+q^2\right) \times\left(2 p^2-3 q^2\right)$
Answer$\left(3 p^2+q^2\right) \times\left(2 p^2-3 q^2\right)$
$=3 p^2\left(2 p^2-3 q^2\right)+q^2\left(2 p^2-3 q^2\right)$
$=6 p^4-9 p^2 q^2+2 p^2 q^2-3 q 4$
$=6 p^4-7 p^2 q^2-3 q^4$
View full question & answer→Question 602 Marks
Using the formula for squaring a binomial, evaluate the following:
$(82)^2$
Answer$(82)^2$
$=(80+2)^2$
$=(80)^2+2 \times 80 \times 2+(2)^2$
$=6400+320+4$
$=6724$
View full question & answer→Question 612 Marks
Write the quotient and remainder when we divide:
$\left(6 x^2-31 x+47\right)$ by $(2 x-5)$
View full question & answer→Question 622 Marks
Using the formula for squaring a binomial, evaluate the following:
$(69)^2$
Answer$(69)^2$
$=(70-1)^2$
$=(70)^2-2 \times 70 \times 1+(1)^2$
$=4900-140+1$
$=4901-140$
$=4761$
View full question & answer→Question 632 Marks
Using the formula for squaring a binomial, evaluate the following:
$(103)^2$
Answer$(103)^2$
$= (100+3)^2$
$= (100)^2+2 \times 100 \times 3+(3)^2$
$= 10000+600+9$
$= 10609$
View full question & answer→Question 642 Marks
Find the following products:
$\left(x^2-a^2\right) \times(x-a)$
Answer$\left(x^2-a^2\right) \times(x-a)$
$=x^2(x-a)-a^2(x-a)$
$=x^3-a x^2-a^2 x+a^3$
View full question & answer→Question 652 Marks
Find the value of:
$\frac{198\times198-102\times102}{96}$
Answer$\frac{198\times198-102\times102}{96}$
$=\frac{(198)^2-(102)^2}{96}$
$=\frac{(198-102)(198+102)}{96}$
$=\frac{300\times96}{96}$
$=300$
View full question & answer→Question 662 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$
$\text{x}^2-\frac{1}{\text{x}^2}$
View full question & answer→Question 672 Marks
Find following products:
$(4 x+5 y)(4 x+5 y)$
Answer$(4 x+5 y)(4 x+5 y)$
$=(4 x+5 y)^2$
$=(4 x)^2+2 \times 4 x \times 5 y+(5 y)^2$
$=16 x^2+25 y^2+40 x y$
View full question & answer→Question 682 Marks
Expand:
$(8 a+3 b)^2$
Answer$(8 a +3 b)^2$
$=(8 a)^2+2 \times 8 a \times 3 b+(3 b)^2$
$=64 a^2+48 a b+9 b^2$
View full question & answer→Question 692 Marks
Divide:
$12 x ^4+8 x ^3-6 x ^2 \text { by }-2 x ^2$
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} $
View full question & answer→Question 702 Marks
Write the quotient and remainder when we divide:
$\left(x^3+1\right)$ by $(x+1)$
View full question & answer→Question 712 Marks
Expand:
$\Big(3\text{m}-\frac{4}{5}\text{n}\Big)^2$
Answer$\Big(3\text{m}-\frac{4}{5}\text{n}\Big)^2$
$=\Big(\text{3m}\Big)^2-2\times3\text{m}\times\frac{4}{5}\text{n}+\Big(\frac{4}{5}\text{n}\Big)^2$
$=9\text{m}^2-\frac{24\text{mn}}{5}+\frac{16}{25}\text{n}^2$
View full question & answer→Question 722 Marks
Divide
$8 x^2 y^2-6 x y^2+10 x^2 y^3 \text { by } 2 x y$
Answer$(8\text{x}^2\text{y}^2 − 6\text{xy}^2 + 10\text{x}^2\text{y}^3 )\div 2\text{xy}$
$\Rightarrow\frac{8\text{x}^2\text{y}^2}{2\text{xy}}− \frac{6\text{xy}^2}{2\text{xy}}+ \frac{10\text{x}^2\text{y}^3}{ 2\text{xy }}$
$\Rightarrow4\text{xy} - 3\text{y} + 5\text{xy}^2$
View full question & answer→Question 732 Marks
Find following products:
$\left(x^2+7\right)\left(x^2+7\right)$
Answer$\left(x^2+7\right)\left(x^2+7\right)$
$=\left(x^2+7\right)^2$
$=\left(x^2\right)^2+7^2+2 \times x^2 \times 7$
$=x^4+49+14 x^2$
View full question & answer→Question 742 Marks
Subtract:
2a - 5b + 2c - 9 from 3a - 4b - c + 6
Question 752 Marks
Find the following products:
$\left(x^2-5 x+8\right) \times\left(x^2+2\right)$
Answer$\left(x^2-5 x+8\right) \times\left(x^2+2\right)$
$=\left(x^2-5 x+8\right) \times x^2+\left(x^2-5 x+8\right) \times 2$
$=x^4-5 x^3+8 x^2+2 x^2-10 x+16$
$=x^4-5 x^3+10 x^2-10 x+16$
View full question & answer→Question 762 Marks
Add:
7x, -3x, 5x, -x, -2x
Answer7x + (-3x) + 5x + (-x) + (-2x)
= 7x - 3x + 5x - x - 2x
= 12x - 6x = 6x
View full question & answer→Question 772 Marks
Add:
$2 x^3-9 x^2+8,3 x^2-6 x-5,7 x^3-10 x+1$ and $3+2 x-5 x^2-4 x^3$
View full question & answer→Question 782 Marks
Add: $4 x^2-7 x y+4 y^2-3,5+6 y^2-8 x y+x^2$ and $6-2 x y+2 x^2-5 y^2$
Answer$4 x^2+4 y^2-7 x y-3$
$x^2+6 y^2-8 x y+5$
$\underline {2 x^2-5 y^2-2 x y+6}$
$7 x^2+5 y^2-17 x y+8$
View full question & answer→Question 792 Marks
Find the following products:
$\left(3 x^2+5 x-9\right) \times(3 x-5)$
Answer$\left(3 x^2+5 x-9\right) \times(3 x-5)$
$=3 x^2(3 x-5 x)+5 x(3 x-5)-9(3 x-5)$
$=9 x^3+15 x^2-27 x-15 x^2-25 x+45$
$=9 x^3-52 x+45$
View full question & answer→Question 802 Marks
Subtract:
$5 y^4-3 y^3+2 y^2+y-1$ from $4 y^4-2 y^3-6 y^2-y+5$
View full question & answer→Question 812 Marks
Find following products:
$(x-4)(x-4)$
Answer$(x-4)(x-4)$
$=(x-4)^2$
$=(x)^2-2 \times x \times 4+(4)^2$
$=x^2-8 x+16$
View full question & answer→Question 822 Marks
Find the following products:
$\left(x^4+y^4\right) \times\left(x^2-y^2\right)$
Answer$\left(x^4+y^4\right) \times\left(x^2-y^2\right)$
$=x^4\left(x^2-y^2\right)+y^4\left(x^2-y^2\right)$
$=x^6-x^4 y^2+x^2 y^4-y^6$
View full question & answer→Question 832 Marks
Find the following products:
$\left(x^3-y^3\right) \times\left(x^2+y^2\right)$
Answer$\left(x^3-y^3\right) \times\left(x^2+y^2\right)$
$=x^3\left(x^2+y^2\right)-y^3\left(x^2+y^2\right)$
$=x^5+x^3 y^2-x^2 y^3-y^5$
View full question & answer→Question 842 Marks
Find the following products:
$\left(x^2-y^2\right) \times(x+2 y)$
Answer$\left(x^2-y^2\right) \times(x+2 y)$
$=x^2(x+2 y)-y^2(x+2 y)$
$=x^3+2 x^2 y-x y^2-2 y^3$
View full question & answer→Question 852 Marks
Find following products:
$(7 a+9 b)(7 a+9 b)$
Answer$=(7 a+9 b)^2$
$=(7 a)^2+(9 b)^2+2 \times 7 a \times 9 b$
$=49 a^2+81 b^2+126 a b$
View full question & answer→Question 862 Marks
Find the value of the expression $\left(9 x^2+24 x+16\right)$, when $x=12$.
Answer$\left(9 x^2+24 x+16\right)$
$=(3 x)^2+2(3 x)(4)+(4)$
$=(3 x+4)^2$
$=(3 \times 12+4)^2$
$=(36+4)^2$
$=(40)^2$
$=1600$
View full question & answer→Question 872 Marks
Find the following products:
$(9 x+5 y) \times(4 x+3 y)$
Answer$(9 x+5 y) \times(4 x+3 y)$
$9 x(4 x+3 y)+5 y(4 x+3 y)$
$=36 x^2+27 x y+20 x y+15 y^2$
$=36 x^2+47 x y+15 y^2$
View full question & answer→Question 882 Marks
Subtract:
$4 p^2+5 q^2-6 r^2+7$ from $3 p^2-4 q^2-5 r^2-6$
View full question & answer→