Akhileshwar Nani has Published 204 Articles

Find the greatest common factor of the terms in the expression $2xyz+3x^2y+4y^2$.

Akhileshwar Nani

Updated on 03-Apr-2023 21:06:43

102 Views

Given:The given expression is $2xyz+3x^2y+4y^2$.To do:We have to find the greatest common factor of the terms in the given expression.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of ... Read More

Find the greatest common factor of the terms in the expression $5a^4+10a^3-15a^2$.

Mathematics Class 8

Akhileshwar Nani

Updated on 03-Apr-2023 21:05:38

69 Views

Given:The given expression is $5a^4+10a^3-15a^2$.To do:We have to find the greatest common factor of the terms in the given expression.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of ... Read More

Find the greatest common factor (GCF/HCF) of the polynomials $14x^3y^5, 10x^5y^3$ and $2x^2y^2$.

Mathematics Class 8

Akhileshwar Nani

Updated on 03-Apr-2023 21:04:58

101 Views

Given:Given polynomials are $14x^3y^5, 10x^5y^3$ and $2x^2y^2$.To do:We have to find the greatest common factor of the given polynomials.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the ... Read More

Show that:
(i) $(3x + 7)^2 - 84x = (3x - 7)^2$
(ii) $(9a - 5b)^2 + 180ab = (9a + 5b)^2$
(iii) $(\frac{4m}{3} - \frac{3n}{4})^2 + 2mn = \frac{16m^2}{9} + \frac{9n^2}{16}$
(iv) $(4pq + 3q)^2 - (4pq - 3q)^2 = 48pq^2$
(v) $(a - b) (a + b) + (b - c) (b + c) + (c - a) (c + a) = 0$

Mathematics Class 8

Akhileshwar Nani

Updated on 03-Apr-2023 21:03:30

41 Views

To do:We have to show that:(i) $(3x + 7)^2 - 84x = (3x - 7)^2$(ii) $(9a - 5b)^2 + 180ab = (9a + 5b)^2$(iii) $(\frac{4m}{3} - \frac{3n}{4})^2 + 2mn = \frac{16m^2}{9} + \frac{9n^2}{16}$(iv) $(4pq + 3q)^2 - (4pq - 3q)^2 = 48pq^2$(v) $(a - b) (a + b) + (b ... Read More

Find the greatest common factor (GCF/HCF) of the polynomials $2x^2$ and $12x^2$.

Mathematics Class 8

Akhileshwar Nani

Updated on 02-Apr-2023 14:48:13

142 Views

Given:Given polynomials are $2x^2$ and $12x^2$.To do:We have to find the greatest common factor of the given polynomials.Solution:HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The highest common factor (HCF) of those numbers is found by finding all common factors of the numbers ... Read More

Evaluate the following:
(i) $102 \times 106$
(ii) $109 \times 107$
(iii) $35 \times 37$
(iv) $53 \times 55$
(v) $103 \times 96$
(vi) $34 \times 36$
(vii) $994 \times 1006$

Mathematics Class 8

Akhileshwar Nani

Updated on 02-Apr-2023 14:44:37

59 Views

Given:(i) $102 \times 106$(ii) $109 \times 107$(iii) $35 \times 37$(iv) $53 \times 55$(v) $103 \times 96$(vi) $34 \times 36$(vii) $994 \times 1006$To do:We have to find the given products.Solution:Here, to find the given products we can use distributive property twice.Distributive Property:The distributive property of multiplication states that when a factor ... Read More

Find the following products:
(i) $(x + 4) (x + 7)$
(ii) $(x - 11) (x + 4)$
(iii) $(x + 7) (x - 5)$
(iv) $(x - 3) (x - 2)$
(v) $(y^2 - 4) (y^2 - 3)$
(vi) $(x + \frac{4}{3}) (x + \frac{3}{4})$
(vii) $(3x + 5) (3x + 11)$
(viii) $(2x^2 - 3) (2x^2 + 5)$
(ix) $(z^2 + 2) (z^2 - 3)$
(x) $(3x - 4y) (2x - 4y)$
(xi) $(3x^2 - 4xy) (3x^2 - 3xy)$
(xii) $(x + \frac{1}{5}) (x + 5)$
(xiii) $(z + \frac{3}{4}) (z + \frac{4}{3})$
(xiv) $(x^2 + 4) (x^2 + 9)$
(xv) $(y^2 + 12) (y^2 + 6)$
(xvi) $(y^2 + \frac{5}{7}) (y^2 - \frac{14}{5})$
(xvii) $(p^2 + 16) (p^2 - \frac{1}{4})$

Mathematics Class 8

Akhileshwar Nani

Updated on 02-Apr-2023 14:44:08

71 Views

To do:We have to find the given products.Solution:Here, to find the given products we can use distributive property twice.Distributive Property:The distributive property of multiplication states that when a factor is multiplied by the sum or difference of two terms, it is essential to multiply each of the two numbers by ... Read More

Find the greatest common factor (GCF/HCF) of the polynomials $2x^3y^2, 10x^2y^3$ and $14xy$.

Mathematics Class 8

Akhileshwar Nani

Updated on 02-Apr-2023 14:43:17

132 Views

Given:Given polynomials are $2x^3y^2, 10x^2y^3$ and $14xy$.To do:We have to find the greatest common factor of the given polynomials.Solution:HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The highest common factor (HCF) of those numbers is found by finding all common factors of the ... Read More

Find the greatest common factor (GCF/HCF) of the polynomials $15a^3, -45a^2$ and $-150a$.

Mathematics Class 8

Akhileshwar Nani

Updated on 02-Apr-2023 14:30:26

97 Views

Given:Given polynomials are $15a^3, -45a^2$ and $-150a$.To do:We have to find the greatest common factor of the given polynomials.Solution:GCF/HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest/highest common factor (GCF/HCF) of those numbers is found by finding all common factors of the ... Read More

Find the greatest common factor (GCF/HCF) of the polynomials $x^3$ and $-yx^2$.

Mathematics Class 8

Akhileshwar Nani

Updated on 02-Apr-2023 14:29:58

120 Views

Given:Given polynomials are $x^3$ and $-yx^2$.To do:We have to find the greatest common factor of the given polynomials.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers ... Read More

About

Akhileshwar Nani has Published 204 Articles