Question
Factorize:
$x^2 - 1 - 2a - a^2$
$x^2 - 1 - 2a - a^2$
✓
Answer
The given expression to be factorized is $x^2 - 1 - 2a - a^2$
Take common $-1$ from the last three terms and then we have
$x^2 - 1 - 2a - a^2$
$= x^2 - (1 + 2a + a^2)$
$= x^2 - {(1)^2 + 2.1.a + (a)^2}$
$= x^2 - (1 + a)^2$
$= (x)^2 - (1 + a)^2$
$= {x + (1 + a)}{x - (1 + a)}$
$= (x + 1 + a)(x - 1 - a)$
We cannot further factorize the expression.
So, the required factorization is $x^2 - 1 - 2a - a^2 = (x + 1 + a)(x - 1 - a).$
Take common $-1$ from the last three terms and then we have
$x^2 - 1 - 2a - a^2$
$= x^2 - (1 + 2a + a^2)$
$= x^2 - {(1)^2 + 2.1.a + (a)^2}$
$= x^2 - (1 + a)^2$
$= (x)^2 - (1 + a)^2$
$= {x + (1 + a)}{x - (1 + a)}$
$= (x + 1 + a)(x - 1 - a)$
We cannot further factorize the expression.
So, the required factorization is $x^2 - 1 - 2a - a^2 = (x + 1 + a)(x - 1 - a).$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where,
p(x) = 2x^3 + 3x^2 - 11x - 3$, $\text{g}(\text{x})=\Big(\text{x}+\frac{1}{2}\Big).$
→p(x) = 2x^3 + 3x^2 - 11x - 3$, $\text{g}(\text{x})=\Big(\text{x}+\frac{1}{2}\Big).$
Solve the following simultaneous equations.
3x – 4y – 15 = 0 ........... (I)
y +x + 2 = 0 ........(II)
3x – 4y – 15 = 0 ........... (I)
y +x + 2 = 0 ........(II)
If $\frac{a}{b}=\frac{2}{3}$, then find the values of the following expressions : $\frac{7 b-4 a}{7 b+4 a}$
→Find the median of the data:
41, 43, 127, 99, 71, 92, 71, 58, 57
41, 43, 127, 99, 71, 92, 71, 58, 57
If $\frac{a}{(x-2 y+3 z)}=\frac{b}{(y-2 z+3 x)}=\frac{c}{(z-2 x+3 y)}$ and $x+\mathrm{y}+\mathrm{z} \neq 0$ then prove that each ratio $=\frac{a+b+c}{2(x+y+z)}$
→Simplify the following products:$(\text{x}^3 -3\text{x}^2-\text{x})(\text{x}^2-3\text{x} + 1)$
→Evaluate:$\Big(\frac{64}{125}\Big)^{-\frac{2}{3}}+\Big(\frac{256}{625}\Big)^{-\frac{1}{4}}+\Big(\frac{3}{7}\Big)^0$
→The circumference of the base of a $10m$ height conical tent is $44m$, calculate the length of canvas used in making the tent if width of canvas is $2m$ $\Big($Use $\pi=\frac{22}{7}\Big).$
→The external dimensions of a closed wooden box are $48cm, 36cm, 30cm$. The box is made of 1.5cm thick wood. How many bricks of size $6cm \times 3cm \times 0.75cm$ can be put in this box?
→In figure, OA and OB are opposite rays:
If x = 25°, what is the value of y?
If x = 25°, what is the value of y?