Question 512 Marks
Using the standard formulae, expand:
$(5 x-3 y)^2$
Answer$25 x^2+9 y^2-30 x y$
View full question & answer→Question 522 Marks
Using the standard formulae, expand:
$\left(6+\frac{5}{x}\right)^2$
Answer$36+\frac{25}{x^2}+\frac{60}{x}$
View full question & answer→Question 532 Marks
Using the standard formulae, expand:
$\left(\frac{x}{3}+\frac{6}{x}\right)^2$
Answer$\frac{x^2}{9}+\frac{36}{x^2}+4$
View full question & answer→Question 542 Marks
Using the standard formulae, expand:
$\left(\frac{2}{5} x+\frac{5}{6} y\right)^2$
Answer$\frac{4}{25} x^2+\frac{25}{36} y^2+\frac{2}{3} x y$
View full question & answer→Question 552 Marks
Using the standard formulae, expand:
$\left(2 x+\frac{1}{3 x}\right)^2$
Answer$4 x^2+\frac{1}{9 x^2}+\frac{4}{3}$
View full question & answer→Question 562 Marks
Using the standard formulae, expand:
$\left(3 x^2 y+z\right)^2$
Answer$9 x^4 y^2+z^2+6 x^2 y z$
View full question & answer→Question 572 Marks
Using the standard formulae, expand:
$\left(2 a^2+3 b\right)^2$
Answer$4 a^4+9 b^2+12 a^2 b$
View full question & answer→Question 582 Marks
If $a=\frac{1}{(a-5)}$, where $a \neq 5$ and $a \neq 0$, find the values of : $\left(a^2+\frac{1}{a^2}\right)$
View full question & answer→Question 592 Marks
If $a=\frac{1}{(a-5)}$, where $a \neq 5$ and $a \neq 0$, find the values of : $\left(a^2-\frac{1}{a^2}\right)$
View full question & answer→Question 602 Marks
If $a=\frac{1}{(a-5)}$, where $a \neq 5$ and $a \neq 0$, find the values of : $\left(a+\frac{1}{a}\right)$
View full question & answer→Question 612 Marks
If $a=\frac{1}{(a-5)}$, where $a \neq 5$ and $a \neq 0$, find the values of : $\left(a-\frac{1}{a}\right)$
View full question & answer→Question 622 Marks
If $\left(a^2-4 a-1\right)=0$ and $a \neq 0$, find the values of : $\left(a^2+\frac{1}{a^2}\right)$
View full question & answer→Question 632 Marks
If $\left(a^2-4 a-1\right)=0$ and $a \neq 0$, find the values of :$\left(a^2-\frac{1}{a^2}\right)$
View full question & answer→Question 642 Marks
If $\left(a^2-4 a-1\right)=0$ and $a \neq 0$, find the values of : $\left(a+\frac{1}{a}\right)$
View full question & answer→Question 652 Marks
If $\left(a^2-4 a-1\right)=0$ and $a \neq 0$, find the values of :$\left(a-\frac{1}{a}\right)$
View full question & answer→Question 662 Marks
Using the standard formulae, expand:
$(\sqrt{2} m+\sqrt{3} n)^2$
Answer$2 m^2+3 n^2+2 \sqrt{6} m n$
View full question & answer→Question 672 Marks
Using the standard formulae, expand:
$(3 x+10 y)^2$
Answer$9 x^2+100 y^2+60 x y$
View full question & answer→Question 682 Marks
Using the standard formulae, expand:
$(4 a+9)^2$
View full question & answer→Question 692 Marks
Simplify : $(3 x+1)^2-(3 x+2)(3 x-1)$
View full question & answer→Question 702 Marks
Simplify : $(5 a+3 b)^2-(5 a-3 b)^2-60 a b$
View full question & answer→Question 712 Marks
Simplify : $\left(3 x-\frac{1}{3 x}\right)^2-\left(3 x+\frac{1}{3 x}\right)\left(3 x-\frac{1}{3 x}\right)$
Answer$2\left(\frac{1}{9 x^2}-1\right)$
View full question & answer→Question 722 Marks
Simplify : $\left(\frac{a}{2 b}+\frac{2 b}{a}\right)^2-\left(\frac{2 b}{a}-\frac{a}{2 b}\right)^2$
View full question & answer→Question 732 Marks
Simplify : $\left(x+\frac{1}{x}\right)^2-\left(x-\frac{1}{x}\right)^2$
View full question & answer→Question 742 Marks
Simplify : $\left(x+\frac{1}{x}\right)^2+\left(x-\frac{1}{x}\right)^2$
Answer$2\left(x^2+\frac{1}{x^2}\right)$
View full question & answer→Question 752 Marks
Simplify : $(a+b)^2-(a-b)^2$
View full question & answer→Question 762 Marks
Simplify : $(a+b)^2+(a-b)^2$
Answer$2\left(a^2+b^2\right)$
View full question & answer→Question 772 Marks
Using the standard formulae, expand:
$(x-5)(2 x-1)(2 x+3)$
Answer$4 x^3-16 x^2-23 x+15$
[Hint.
$\begin{aligned}(x-5)(2 x-1)(2 x+3) & =(x-5)\left[4 x^2+6 x-2 x-3\right] \\ & =(x-5)\left(4 x^2+4 x-3\right) \\ & =x\left(4 x^2+4 x-3\right)-5\left(4 x^2+4 x-3\right) \text { etc.] }\end{aligned}$
View full question & answer→Question 782 Marks
Using the standard formulae, expand:
$(x-2)(x-3)(x+4)$
View full question & answer→Question 792 Marks
Using the standard formulae, expand:
$(x+y)(x-y)\left(x^2+y^2\right)$
View full question & answer→Question 802 Marks
Using the standard formulae, expand:
$(2-x)(2+x)\left(4+x^2\right)$
View full question & answer→Question 812 Marks
Using the standard formulae, expand:
$\left(2 x^2+\frac{3}{x^2}\right)\left(2 x^2-\frac{3}{x^2}\right)$
Answer$4 x^4-\frac{9}{x^4}$
View full question & answer→Question 822 Marks
Using the standard formulae, expand:
$\left(5 x+\frac{1}{5 x}\right)\left(5 x-\frac{1}{5 x}\right)$
Answer$25 x^2-\frac{1}{25 x^2}$
View full question & answer→Question 832 Marks
Using the standard formulae, expand:
$(3 a+2 b)(3 a-2 b)$
View full question & answer→Question 842 Marks
Using the standard formulae, expand:
$(3-7 a)(3+4 a)$
View full question & answer→Question 852 Marks
Using the standard formulae, expand:
$(5 x-4 y)(5 x+3 y)$
Answer$25 x^2-5 x y-12 y^2$
View full question & answer→Question 862 Marks
Using the standard formulae, expand:
$(9+2 x)(9-3 x)$
View full question & answer→Question 872 Marks
If $x^2+y^2+\frac{1}{x^2}+\frac{1}{y^2}=4$, then find the value of $x^2+y^2$.
View full question & answer→Question 882 Marks
If $\frac{1}{x+y}=\frac{1}{x}+\frac{1}{y},(x \neq 0, y \neq 0, x \neq y)$, then find the value of $x^3-y^3$.
View full question & answer→Question 892 Marks
If $x^4+\frac{1}{x^4}=119, x>1$, then find the value of $x^3-\frac{1}{x^3}$.
View full question & answer→Question 902 Marks
Write down the following product:
$\left(3 a^2-b^2\right)\left(2 a^2+5 b^2\right)$
Answer$6 a^4+13 a^2 b^2-5 b^4$
View full question & answer→Question 912 Marks
Write down the following product:
(2y - 3) (3y - 5)
Question 922 Marks
Write down the following product:
(7m - 2) (4m + 3)
Question 932 Marks
Write down the following product:
(2x + 3) (3x + 5)
Question 942 Marks
Write down the following product:
(6 - x) (x + 5)
Question 952 Marks
Write down the following product:
$\left(3-x^2\right)\left(5+x^2\right)$
View full question & answer→Question 962 Marks
Write down the following product:
$\left(x^2+1\right)\left(x^3+2\right)$ [Hint. Put $\left.x^2=y\right]$
View full question & answer→Question 972 Marks
Write down the following product:
(5 - xy) (2 + xy)
Question 982 Marks
Write down the following product:
(ab + 3) (ab - 2)
Question 992 Marks
Write down the following product:
(y - 7) (y + 4)
Question 1002 Marks
Write down the following product:
(2 - x) (4 - x)