Question
Factorise:
$16 x^2+4 y^2+9 z^2-16 x y-12 y z+24 x z$
$16 x^2+4 y^2+9 z^2-16 x y-12 y z+24 x z$
✓
Answer
We have:
$16 x^2+4 y^2+9 z^2-16 x y-12 y z+24 x z$
$=(4 x)^2+(-2 y)^2+(3 z)^2+2(4 x)(-2 y)+2(-2 y)(3 z)+2(3 z)(4 x)$
$=(4 x-2 y+3 z)^2\left[\text { using } a^2+b^2+c^2+2 a b+2 b c+2 c a=(a+b+c)^2\right]$
Hence, $16 x^2+4 y^2+9 z^2-16 x y-12 y z+24 x z=(4 x-2 y+3 z)^2$
$16 x^2+4 y^2+9 z^2-16 x y-12 y z+24 x z$
$=(4 x)^2+(-2 y)^2+(3 z)^2+2(4 x)(-2 y)+2(-2 y)(3 z)+2(3 z)(4 x)$
$=(4 x-2 y+3 z)^2\left[\text { using } a^2+b^2+c^2+2 a b+2 b c+2 c a=(a+b+c)^2\right]$
Hence, $16 x^2+4 y^2+9 z^2-16 x y-12 y z+24 x z=(4 x-2 y+3 z)^2$
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
Factorise: $\frac{3}{5}\text{x}^2-\frac{19}{5}\text{x}+4$
→$B E$ and $C F$ are two equal altitudes of a triangle $A B C$. Using $RHS$ congruence rule, prove that a triangle $A B C$ is isosceles.
→The outer diameter of a spherical shell is $12\ cm$ and its inner diameter is $8\ cm$. Find the volume of metal contained in the shell. Also, find its outer surface area. $\big(\text{Take}\ \pi=\frac{22}{7}\big).$
→ Simplify the following:
$\frac{7.83\times7.83-1.17\times1.17}{6.66}$
→$\frac{7.83\times7.83-1.17\times1.17}{6.66}$
Examine whether the following numbers are rational or irrational. $\sqrt[3]{5}\times\sqrt[3]{25}$
→Multiply: $3\sqrt{5}$ by $2\sqrt{5}$
→A hemispherical bowl of internal radius $9\ cm$ contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3cm and height $4\ cm$ How many bottles required to empty the bowl?
→Express the following equation in the form $ax + by + c = 0$ and indicate the values of $a, b, c$ in case.$2\text{x}-\frac{\text{y}}{5}+6=0$
→Hameed has built a cubical water tank with lid for his house, with each other edge $1.5 \ m$ long. He gets the outer surface of the tank excluding the base, covered with square tiles of side $25 \ cm$. Find how much he would spend for the tiles if the cost of tiles is $₹ 360$ per dozen.
→In the adjoining figure, $ABCD$ is a trapezium in which $AB \| DC$ and its diagonals $AC$ and $BD$ intersect at $O.$
Prove that $\text{ar}(\triangle\text{AOD})=\text{ar}\triangle\text{BOC}.$
→Prove that $\text{ar}(\triangle\text{AOD})=\text{ar}\triangle\text{BOC}.$