Expansion of (x+a)(x+b)

Q.

If a+b+c=0

Then find the value of a³+b³+c³

Q. if x+1/x=2 then find the value of x^{100}+1/x^{100} , find attached solutio

Q. If x + y = 12 and xy = 14 then find the value of (x2 + y2).

Q. Let a, b anc be real numbers such that a-7b+8c=4 and 8a+4b-c=7 then the value of a^2-b^2+c^2is:

Q.

Evaluate: $104\times 105$

1. 10920

2. 10900

3. 10290

4. 10090

Q. If $a^2+b^2=20$ and $ab=8$, find the value of $(a+b)$

1. 5
2. None of the above
3. 6
4. 4

Q.

There are two numbers such that their product is 12 and the sum of the numbers is 8.

Find the sum of their squares.

1. 40

2. 52

3. 4

4. 22

Q.

Use suitable identities and find

(51)² - (49)²

Q.

If $2x-3y=4$, the value of $8x^3-27y^3-72xy$is

1. $32$

2. $16$

3. $128$

4. $64$

Q.

Evaluate :

(i) $(3x+\frac{1}{2})(2x+\frac{1}{3})$

(ii) $(2a+0.5)(7a-0.3)$

(iii) $(9-y)(7+y)$

(iv) $(2-z)(15-z)$

(v) $(a^2+5)(a^2-3)$

(vi) $(4-ab)(8+ab)$

(vii) $(5xy-7)(7xy+9)$

(viii) $(3a^2-4b^2)(8a^2-3b^2)$

Q. Use a suitable identity to get each of the following products
(3a - 1\2) (3a- 1/2)

Q.

Find the value using identities : $182\times 182-2\times 182\times 62+62\times 62$

Q. Expand $(x-8)(x-10)$.

1. $x^2-18x-80$
2. $x^2+18x-80$
3. $x^2-18x+80$
4. $x^2+18x+80$

Q. 45. x³+12x/6x²+8=y³+27y/9y²+27 using components and dividendo find x:y

Q.

(x+2y)²-4 (2x-y)²

Q. $136\times 107$ = (using identities)

1. 14552
2. 14551
3. 14562
4. 13552

Q.

Write the coefficient of $a$ in $-3a$

Q. Evaluate using identity (9.7)²

Q. Factories

Q. Expand: $(p+8)(p-3)$

1. $p^2+5p-24$
2. $2p^2+11p-24$
3. $p^2-5p+24$
4. $-p^2-11p-4$

Q.

Using identity, evaluate (x - 3)(x + 3).

1. 2x² - 9

2. x² - 3

3. x² - 9

4. x² + 9

Q.

Use the identity $(x+a)(x+b)=x^2+(a+b)x+ab$ to find the following products:
$(abc-4)(abc-2)$

1. $a^2{b}^2{c}^2-6abc-8$

2. $a^2{b}^2{c}^2-6abc+8$

3. $a^2{b}^2{c}^2+6a+8$

4. $a^2{b}^2{c}^2-6a-8$

Q.

What is the coefficient of x in 10x^3

Q.

$1003\times 999=$ ___

Q.

Simplify and solve the following linear equation:
$3(5z-7)-2(9z-11)=4(8z-13)-17$

Q.

Use direct method to ecaluate the following products :

(i) (x + 8)(x + 3)

(ii) (y + 5)(y - 3)

(iii) (a- 8)(a+ 2)

(iv) (b - 3)(b - 5)

(v) (3x - 2y)(2x + y)

(vi) (5a + 16)(3a -7)

(vii) (8 - b)(3 + b)

Q. Find the product : ( x + 1 ) ( x - 1) ( x^2 +1)

Q. Question 41

In the question given below, fill in the blank to make the statement true:

$(x+a)(x+b)=x^2+(a+b)x+$ ___

Q.

Express the following expressions as a perfect square : $4a^2+12ab+9b^2$

Q.

Factories the following expressions.
(i) $7x-42$