State True or False, if the expansion of the following expression is:
$(3 x - 2 y - z)^{2} =$ $9 x^{2} + 4 y^{2} + z^{2} - 12 x y + 4 y z - 6 x z$

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A True
We know that,
$(a - b - c)^{2} = a^{2} + b^{2} + c^{2} - 2 a b + 2 b c - 2 c a$
So,
$(3 x - 2 y - z)^{2} = (3 x)^{2} + (2 y)^{2} + (z)^{2} - 2 \times (3 x) \times (2 y) + 2 \times (2 y) \times (z) - 2 \times (z) \times (3 x)$
$(3 x - 2 y - z)^{2} = 9 x^{2} + 4 y^{2} + z^{2} - 12 x y + 4 y z - 6 z x$
Hence the answer is True.

Suggest Corrections

Similar questions

(x + 2 y + z)^{2}

2 x + 2 y - z)^{2}

(x + 2 y + 3 z)^{2}

27 x^{3} + y^{3} + z^{3} - 9 x y z

= (3 x + y + z) [(9 x^{2} + y^{2} + z^{2} - 3 x y - y z - 3 z x)]

(3 x - \frac{1}{2 y}) (3 x + \frac{1}{2 y})

9 x^{2} - \frac{1}{4 y^{2}}

Join BYJU'S Learning Program