Question

Q1. ਵਿਅੰ ਜਕ 4x + 3y², 7xy – 4y² ਅਤੇ 6x2 – x ਦਾ ਜੋੜਫਲ ਕੀ ਹੈ ? What is the sum of the expressions 4x + 3y², 7xy – 4y² and 6x 2 – x ? a) 6x 2 + 3x + 7xy + y 2 b) 6x 2 + 3x – 7xy – y 2 c) 6x 2 + 3x – 7xy + y 2 d) 6x 2 + 3x + 7xy − y² Q2. ਵਿਮਿਵਲਖਤ ਵਿਿੱ ਚੋਂ ਵਕਹੜੀਆਂ ਸਮਾਿ ਪਦਾਂ ਹਿ ? Which of the following are like terms? (a) 5xyz2 , – 3xy2 z (b) – 5xyz2 , 7xyz2 (c) 5xyz2 , 5x2 yz (d) 5xyz2 , x2 y 2 z 2 Q3. 6x²y² ਵਿਿੱ ਚ xy ਦਾ ਗੁਣਾਂਕ ਹੈ ? The coefficient of xy in 6x²y² is (a) xy (b) 2xy (c) 3xy (d) 6xy Q4. -x +y ਤੋਂ 7x +y ਿ ੰ ਘਟਾਉਣਾ Subtracting 7x +y from –x +y gives (a) 6x+2y (b) 8x+2y (c) -8x (d) 8x Q5. ab-bc, bc-ca, ca-ab ਦਾ ਜੋੜ ਹੈ ? The addition of ab-bc, bc-ca, ca-ab is (a) 3ab+3bc+3ca (b) 0 (c) ab+bc+ca (d) ab-bc+ca Q6. (x+3)(x+3) ਪਤਾ ਕਰਿ ਲਈ ਵਕਹੜਾ ਤਤਸਮਕ ਉਪਯੁਕਤ ਹੈ? The suitable identity to find (x+3)(x+3) is (a) (a+b)2 (b) (a – b)2 (c) a 2 – b 2 (d) (x+a)(x+b) Q7. (m+3)(m+2) ਦਾ ਮੁਿੱ ਲ ਪਤਾ ਕਰਿ ਲਈ ਵਕਹੜਾ ਤਤਸਮਕ ਿਰਵਤਆ ਵਗਆ ਹੈ ? Which identity is used to evaluate (m+3)(m+2). (a) (x+a)(x+b)=x2 +(a+b)x+ab (b) (a+b)2 =a2 +2ab+b2 (c) (a-b)2 =a2 -2ab+b2 (d) a2 – b 2 =(a+b)(a-b) Q8. 9x – 7xy ਦਾ ਿਰਗ ਹੈ । Square of 9x – 7xy is (a) 81x2 + 49x2 y 2 (b) 81x2 – 49x2 y 2 (c) 81x2 + 49x2 y 2 –126x2 y (d) 81x2 + 49x2 y 2 – 63x2 y Q9. 6a2 – 7b + 5ab ਅਤੇ 2ab ਦਾ ਗੁਣਿਫਲ ਹੈ । Product of 6a2 – 7b + 5ab and 2ab is (a) 12a3 b – 14ab2 + 10ab (b) 12a3 b – 14ab2 + 10a2 b 2 (c) 6a2 – 7b + 7ab (d) 12a2 b – 7ab2 + 10ab Q10. ਜੇਕਰ ਆਇਤ ਦਾ ਖੇਤਰਫਲ ‘xy’ ਹੈ ਵਜਿੱ ਥੇ ‘x’ ਲੰ ਬਾਈ ਅਤੇ‘y’ ਚੌੜਾਈ ਹੈ। ਜੇ ਆਇਤ ਦੀ ਲੰ ਬਾਈ 5 ਇਕਾਈ ਿਧਾਈ ਜਾਂਦੀ ਹੈ ਅਤੇ ਚੌੜਾਈ 3 ਇਕਾਈ ਘਿੱਟ ਜਾਂਦੀ ਹੈ, ਤਾਂ ਆਇਤਕਾਰ ਦਾ ਿਿਾਂ ਖੇਤਰ ਹੋਿੇਗਾ ? The area of a recatangle is ’xy’ where ‘ x’ is length and ‘y’ is breadth. If the length of rectangle is increased by 5 units and breadth is decreased by 3 units, the new area of rectangle will be (a) (x-y)(x+3) (b) xy+15 (c) (x+5)(y-3) (d) xy +5-3​

Answer 1

Step-by-step explanation:

please mark aa brain list

Answer 2

Given:

1. The expressions: $4x+3y^{2}, 7xy-4y^{2}$ and $6x^{2} -x$

2. $5xyz^{2}$ and $-3xy^{2} z$, $-5xyz^{2}$ and $7xyz^{2}$, $5xyz^{2}$ and $5x^{2} yz$, $5xyz^{2}$ and $x^{2} y^{2} z^{2}$

3. The term $6x^{2} y^{2}$

4. The expressions: $7x+y$ and $-x+y$

5. The terms: $ab-bc,bc-ca,ca-ab$

6. The expression: $(x+3)(x+3)$

7. The expression:  $(m+3)(m+2)$

8. The expression: $9x-7xy$

9. The expressions:  $6a^{2} -7b+5ab$ and $2ab$

10. Area of rectangle = xy

Increase in the length of rectangle = 5 units

Decrease in the breadth of rectangle = 3 units

To find:

1. Sum of the expressions.

2. Like terms.

3. Coefficient of $xy$

4. Difference between the expressions.

5. Sum of the terms.

6. A suitable identity.

7. A suitable identity.

8. Square of the expression.

9. Product of the two expressions.

10. New area of the rectangle.

Solution:

1. Given that the expressions: $4x+3y^{2}$,   $7xy-4y^{2}$,   $6x^{2} -x$.

To determine the sum of these expressions, add them. Group the like terms and add them to calculate the sum.

$4x+3y^{2}+7xy-4y^{2} +6x^{2} -x$

$=6x^{2}+(4x-x)+7xy+(3y^{2} -4y^{2} )$

$=6x^{2}+3x+7xy-y^{2}$

2. Like terms are those terms whose variables with any powers are the same. From the given choices, option (b) is the correct answer because the variables are $x,y,z^{2}$ and they are the same in both terms, whereas in other options the variables and their exponents are not the same. Hence, the like terms are $-5xyz^{2}$ and $7xyz^{2}$.

3. $6x^{2} y^{2}$ can be written as $6xy(xy)$. A coefficient is any quantity or number multiplied by variables. Here, we are asked to find the coefficient of $xy$. If we remove $xy$ from the term, then the remaining is the coefficient which is $6xy$. Hence, the coefficient of $xy$ in $6x^{2} y^{2}$ is $6xy$.

4. While subtracting $7x+y$ from $-x+y$, we group the like terms and subtract them.

$-x+y-(7x+y)$

$=-x+y-7x-y$

$=-x-7x+y-y$

$=-8x$

5. On adding $ab-bc, bc-ca, ca-ab$ we first group the like terms and then add them to get the sum as

$ab-bc+bc-ca+ca-ab$

$=ab-ab-bc+bc-ca+ca$

$=0$

6. $(x+3)(x+3)$ is the expanded form of $(x+3)^{2}$ where $(x+3)$ is multiplied twice. $(x+3)^{2}$ is similar to the identity $(a+b)^{2}$ where $a=x,b=3$. Thus, option (a) is correct.

7. $(m+3)(m+2)$ does not follow the identities of $(a+b)^{2},(a-b)^{2}, (a+b)(a-b)$. It only follows $(x+a)(x+b)=x^{2} +(a+b)x+ab$

where, $x=m,a=3,b=2$.

8. By squaring $9x-7xy$ it means, multiplying the number with itself.

$(9x-7xy)^{2}$

$=(9x-7xy)(9x-7xy)$

Multiply the first term in the first bracket with each term in the second bracket and then multiply the second term in the first bracket with each term in the second bracket

$=(9x*9x)+(9x)*(-7xy)+(-7xy)*(9x)+(-7xy)*(-7xy)$

$=81x^{2} -63x^{2} y-63x^{2} y+49x^{2} y^{2}$

$=81x^{2} +49x^{2} y^{2}-126x^{2} y$

9. The product of the terms $6a^{2} -7b+5ab$ and $2ab$ can be obtained by multiplying the first expression with the second term.

$(6a^{2} -7b+5ab)*2ab$

Multiply $2ab$ with each term inside the bracket.

$=12a^{3}b-14ab^{2}+10a^{2} b^{2}$

10. The length of rectangle = $x$ units

The breadth of rectangle = $y$ units

Area of the rectangle = length × breadth

$Area=xy$

New length = $x+5$ units

New breadth = $y-3$ units

∴ New area = New length × new breadth

New Area = $(x+5)(y-3)$

The following are the answers:

1. Sum of the expressions $4x+3y^{2}$,   $7xy-4y^{2}$,   $6x^{2} -x$ is $6x^{2}+3x+7xy-y^{2}$. Option (d).

2. The like terms are $-5xyz^{2}$ and $7xyz^{2}$. Option (b).

3. The coefficient of $xy$ in $6x^{2} y^{2}$ is $6xy$. Option (d).

4. Subtraction of  $7x+y$ from $-x+y$ gives $-8x$. Option (c).

5. Addition of $ab-bc, bc-ca, ca-ab$ gives $0$. Option (b).

6. $(x+3)(x+3)$ is similar to the identity $(a+b)^{2}$ . Option (a).

7. $(m+3)(m+2)$ is similar to the identity $(x+a)(x+b)=x^{2} +(a+b)x+ab$ . Option (a).

8. Squaring $9x-7xy$ gives $81x^{2} +49x^{2} y^{2}-126x^{2} y$. Option (c).

9. Product of the terms $6a^{2} -7b+5ab$ and $2ab$ gives $12a^{3}b-14ab^{2}+10a^{2} b^{2}$

Option (b).

10. New Area = $(x+5)(y-3)$. Option (c).