Question
Write the following in the expanded form:
$(a b+b c+c a)^2$
$(a b+b c+c a)^2$
✓
Answer
We have,
$(a b+b c+c a)^2=(a b)^2+(b c)^2+(c a)^2+2(a b)(b c)+2(b c)(c a)+2(a b)(c a)$
${\left[\therefore(x+y+z)^2=x^2+y^2+z^2+2 x y+2 y z+2 x z\right]}$
$=a^2 b^2+b^2 c^2+c^2 a^2+2(a c) b^2+2(a b)(c)^2+2(b c)(a)^2$
$(a b+b c+c a)^2=a^2 b^2+b^2 c^2+c^2 a^2+2 a c b^2+2 a b c^2+2 b c a^2$
$(a b+b c+c a)^2=(a b)^2+(b c)^2+(c a)^2+2(a b)(b c)+2(b c)(c a)+2(a b)(c a)$
${\left[\therefore(x+y+z)^2=x^2+y^2+z^2+2 x y+2 y z+2 x z\right]}$
$=a^2 b^2+b^2 c^2+c^2 a^2+2(a c) b^2+2(a b)(c)^2+2(b c)(a)^2$
$(a b+b c+c a)^2=a^2 b^2+b^2 c^2+c^2 a^2+2 a c b^2+2 a b c^2+2 b c a^2$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Write the following in the expanded form:
$(a+2 b+c)^2$
→$(a+2 b+c)^2$
Factorise:
$x^2+20 x-69$
→$x^2+20 x-69$
A three-wheeler scooter charges ₹ 15 for first kilometer and ₹ 8 each for every subsequent kilometer. For a distance of x km, an amount of y is paid. Write the linear equation representing the above information.
Find $p(0), p(1)$ and $p(2)$ of the polynomial: $p ( t ) = 2 + t + 2 t ^ { 2 } - t ^ { 3 }$
→Factorise:
$15 x^2-x-28$
→$15 x^2-x-28$
Is the product of a rational and an irrational number always irrational? Give an example.
$A B C D$ is a quadrilateral in which $A D=B C$ and $\angle D A B=\angle C B A$ : Prove that:
i. $\triangle A B D \cong \triangle B A C$
ii. $B D=A C$
iii. $\angle ABD =\angle BAC$
→i. $\triangle A B D \cong \triangle B A C$
ii. $B D=A C$
iii. $\angle ABD =\angle BAC$
In the we have $\angle\text{ABC}=\angle\text{ACB},\angle3=\angle4$ Show that $\angle1=\angle2$ 
→Multiply: $3\sqrt{28}$ by $2\sqrt{7}$
→The mean of $31$ results is $60$. If the mean of the first $16$ results is $58$ and that of the last $16$ results is $62$, find the $16^{\text {th}}$ result.
→