(x±a)(x±b) = x²±(a+b)x+ab.

Q.

Evaluate the following products without multiplying directly: 104 × 96

Q.

Verify :

x^{​​​​​​3} + y^{​​​​​​3} = (x + y) (x^{​​​​​​2} + y^{​​​​​​2} – xy)

Q.

Factorise: $z-7+7xy-xyz$.

Q.

If a=2, b=3 then find the value of (a^{​​​​​b}+b^{​​​​​​a})^-1

Q.

Question 94

Solve the following:

The sum of four consecutive integers is 266. What are the integers?

Q.

If x+y+z=1, xy+yz+zx=-1 and xyz=-1 , x³+y³+z³=?

Q.

Multiply 9x²+25y²+15xy+12x-20y+16 by 3x-5y-4 using suitable identity

Q. Question 10
Verify whether the following are true or false.
(i) -3 is a zero of x - 3
(ii) $-\frac{1}{3}$ is a zero of 3x + 1
(iii) $-\frac{4}{5}$ is a zero of 4 - 5y
(iv) 0 and 2 are the zeroes of $t^2–t$
(v) -3 is a zero of $y^2+y–6$

Q. If 9 + (81)^x = 1/27^x-3 , find x

Q. Simplify:

(i) (a +b + c)² + (a − b + c)²

(ii) (a +b + c)² − (a − b + c)2

(iii) (a +b + c)² + (a − b + c)² + (a +b − c)²

(iv) (2x + p − c)² − (2x − p + c)²

(v) (x² + y² − z²) − (x² − y² + z²)²

Q. If (16)^2x+3 =(64)^x+3, then 4^2x-2 =

(a) 64

(b) 256

(c) 32

(d) 512

Q.

Simplify $a(a^2+a+1)+5$and find its value for$a=0,a=1anda=-1$.

Q. Solve for : 9×(81)^x=1÷27^x-2

Q.

If x+y=7 and x*y=12 find x³+y³

Q. $\frac{5^{n+2}-6\times 5^{n+1}}{13\times 5^n-2\times 5^{n+1}}$ is equal to

(a) $\frac{5}{3}$

(b) $-\frac{5}{3}$

(c) $\frac{3}{5}$

(d) $-\frac{3}{5}$

Q. If (2³)² = 4^x, then 3^x =

(a) 3
(b) 6
(c) 9
(d) 27

Q. Write the value of the determinant $\left|\begin{array}{ccc}x+y& y+z& z+x\\ z& x& y\\ -3& -3& -3\end{array}\right|$.

Q. Find a quadratic polynomial whose zeros are $3$ and $2$.

Q. Simplify: (a+2b+3c)² - (a-2b-3c)² - 6b² - 9bc

Q.

x²-qx-p²+5pq-6q²

^{ans (x-p-2q)(x+p-3q)}

Q. Simplify each of the following expressions:

(i) $(x+y+z{)}^2+{\left(x+\frac{y}{2}+\frac{z}{3}\right)}^2-{\left(\frac{x}{2}+\frac{y}{3}+\frac{z}{4}\right)}^2$

(ii) (x + y− 2z)² − x² − y² − 3z² + 4xy

(iii) (x²− x + 1)² − (x² + x + 1)²

Q.

If (x+y)^3-(x-y)^3-6y(x^2-y^2)=ky^2, find k

Q. Simplify each of the following:

(i) (x+3)³ + (x−3)³

(ii) ${\left(\frac{x}{2}+\frac{y}{3}\right)}^3-{\left(\frac{x}{2}-\frac{y}{3}\right)}^3$

(iii) ${\left(x+\frac{2}{x}\right)}^3+{\left(x-\frac{2}{x}\right)}^3$

(iv) (2x − 5y)³ − (2x + 5y)³

Q. If $8^{x+1}$ = 64 , what is the value of $3^{2x+1}$ ?

(a) 1
(b) 3
(c) 9
(d) 27

Q.

x + y = 10, x^2 + y^2 = 58 then x^3 + y^3 = ?

Q. If x^b × y = 2x - 3y^2 , then find the value of (1/2)^b × 1/root3

Q. If 3^x-1 = 9 and 4^y+2 = 64, what is the value of $\frac{x}{y}$ ?

Q. Assuming that x, y, z are positive real numbers, simplify each of the following:

(i) ${\left(\sqrt{x^{-3}}\right)}^5$

(ii) $\sqrt{x^3{y}^{-2}}$

(iii) $(x^{-2/3}{y}^{-1/2}{)}^2$

(iv) $(\sqrt{x}{)}^{-2/3}\sqrt{y^4}÷\sqrt{x{y}^{-1/2}}$

(v) $\sqrt[5]{243x^{10}{y}^5{z}^{10}}$

(vi) ${\left(\frac{x^{-4}}{y^{-10}}\right)}^{5/4}$

(vii) ${\left(\frac{\sqrt{2}}{\sqrt{3}}\right)}^5{\left(\frac{6}{7}\right)}^2$

Q. If x = 3 and y = − 1, find the values of each of the following using in identify:

(i) (9y² − 4x²) (81y⁴ +36x²y² + 16x⁴)

(ii) $\left(\frac{3}{x}-\frac{x}{3}\right)\left(\frac{x^2}{9}+\frac{9}{x^2}+1\right)$

(iii) $\left(\frac{x}{7}+\frac{y}{3}\right)\left(\frac{x^2}{49}+\frac{y^2}{9}-\frac{xy}{21}\right)$

(iv) $\left(\frac{x}{y}-\frac{y}{3}\right)\frac{x^2}{16}+\frac{xy}{12}+\frac{y^2}{9}$

(v) $\left(\frac{5}{x}+5x\right)$ $\left(\frac{25}{x^2}-25+25x^2\right)$

Q.

Find the following products:

(i) (3x + 2y + 2z) (9x² + 4y² + 4z² − 6xy − 4yz − 6zx)

(ii) (4x − 3y + 2z) (16x² + 9y² + 4z² + 12xy + 6yz − 8zx)

(iii) (2ab − 3b − 2c) (4a² + 9b² +4c² + 6 ab − 6 bc + 4ca)

(iv) (3x − 4y + 5z) (9x² +16y² + 25z² + 12xy −15zx + 20yz)