Question

please solve any one part from them.I do not want direct answers

Answer 1

1) (x² + 3) ( x² - 3)
by identity ( a²-b²)= (a+b) (a-b)
x²-3²= x² -9 this is the answer

Answer 2

4) The products using the identity is given below :

a) $(x^2+3)(x^2-3)=x^4-9$

b) $(3a+7b)(3a-7b)=9a^2-49b^2$

c) $(\frac{a}{4}+\frac{2b}{7})(\frac{a}{4}+\frac{2b}{7})=\frac{a^2}{16}+\frac{4b^2}{49}+\frac{ab}{7}$

d) $(7p-6q)(7p+6q)=49p^2-36q^2$

e)  $(2xy+7yz)(2xy+7yz)=4x^2y^2+49y^2z^2+28xy^2z$

f) $(3m-4n)(3m-4n)=9m^2+16n^2-24mn$

g) $(4pq+m^2)(4pq-m^2)=16p^2q^2-m^4$

h) $(12a-6b)(12a+4b)=144a^2-24ab-24b^2$

i) $(7x+3z)(7x-3z)=49x^2-9z^2$

Step-by-step explanation:

4) a)

• Given expression is $(x^2+3)(x^2-3)$
• To find the value of the given expression :
• The given expression is of the form $(a^2-b^2)=(a+b)(a-b)$
• $(x^2+3)(x^2-3)$
• $=(x^2)^2-3^2$  here a=$x^2$ and b=3
• $=x^4-9$

• Therefore $(x^2+3)(x^2-3)=x^4-9$

b)

• Given expression is $(3a+7b)(3a-7b)$
• To find the value of the given expression :
• The given expression is of the form $(a^2-b^2)=(a+b)(a-b)$
• $(3a+7b)(3a-7b)$ here a=3a and b=7b
• $=(3a)^2-(7b)^2$
• $=9a^2-49b^2$
• Therefore $(3a+7b)(3a-7b)=9a^2-49b^2$

c)

• Given expression is $(\frac{a}{4}+\frac{2b}{7})(\frac{a}{4}+\frac{2b}{7})$
• To find the value of the given expression :
• $(\frac{a}{4}+\frac{2b}{7})(\frac{a}{4}+\frac{2b}{7})$
• $=(\frac{a}{4}+\frac{2b}{7})^2$
• The given expression is of the form $(a+b)^2=a^2+b^2+2ab$
• $=(\frac{a}{4})^2+(\frac{2b}{7})^2+2(\frac{a}{4})(\frac{2b}{7})$ here a=$\frac{a}{4}$ and $b=\frac{2b}{7}$
• $=\frac{a^2}{16}+\frac{4b^2}{49}+\frac{ab}{7}$
• Therefore $(\frac{a}{4}+\frac{2b}{7})(\frac{a}{4}+\frac{2b}{7})=\frac{a^2}{16}+\frac{4b^2}{49}+\frac{ab}{7}$

d)

• Given expression is $(7p-6q)(7p+6q)$
• To find the value of the given expression :
• The given expression is of the form $(a^2-b^2)=(a+b)(a-b)$
• $(7p-6q)(7p+6q)$ here a=7p and b=6q
• $=(7p)^2-(6q)^2$
• $=49p^2-36q^2$
• Therefore $(7p-6q)(7p+6q)=49p^2-36q^2$

e)

• Given expression is $(2xy+7yz)(2xy+7yz)$
• To find the value of the given expression :
• $(2xy+7yz)(2xy+7yz)$
• $=(2xy+7yz)^2$
• The given expression is of the form $(a+b)^2=a^2+b^2+2ab$
• $=(2xy)^2+(7yz)^2+2(2xy)(7yz)$
• $=4x^2y^2+49y^2z^2+28xy^2z$ here a=2xy and b=7yz
• Therefore $(2xy+7yz)(2xy+7yz)=4x^2y^2+49y^2z^2+28xy^2z$

f)

• Given expression is $(3m-4n)(3m-4n)$
• To find the value of the given expression :
• $(3m-4n)(3m-4n)$
• $=(3m-4n)^2$
• The given expression is of the form $(a-b)^2=a^2+b^2-2ab$
• $=(3m)^2+(4n)^2-2(3m)(4n)$
• $=9m^2+16n^2-24mn$ here a=3m and b=4n
• Therefore $(3m-4n)(3m-4n)=9m^2+16n^2-24mn$

g)  

• Given expression is $(4pq+m^2)(4pq-m^2)$
• To find the value of the given expression :
• The given expression is of the form $(a^2-b^2)=(a+b)(a-b)$
• $(4pq+m^2)(4pq-m^2)$
• $=(4pq)^2-(m^2)^2$ here a=4pq and b=$m^2$
• $=16p^2q^2-m^4$
• Therefore $(4pq+m^2)(4pq-m^2)=16p^2q^2-m^4$

h)

• Given expression is $(12a-6b)(12a+4b)$
• To find the value of the given expression :
• The given expression is of the form $(x+a)(x+b)=x^2+(a+b)x+ab$
• $(12a-6b)(12a+4b)$
• $=(12a)^2+(-6b+4b)(12a)+(-6b)(4b)$ here x=12a, a=-6b and b=4b
• $=144a^2-2b(12a)-24b^2$
• $=144a^2-24ab-24b^2$
• Therefore $(12a-6b)(12a+4b)=144a^2-24ab-24b^2$

i)

• Given expression is $(7x+3z)(7x-3z)$
• To find the value of the given expression :
• The given expression is of the form $(a^2-b^2)=(a+b)(a-b)$
• $(7x+3z)(7x-3z)$ here a=7x and b=3z
• $=(7x)^2-(3z)^2$
• $=49x^2-9z^2$
• Therefore $(7x+3z)(7x-3z)=49x^2-9z^2$