Question
Factorise the following:$4x^2 - 12ax - y^2- z^2 - 2yz + 9a^2$
✓
Answer
$4x^2 - 12ax - y^2 - z^2 - 2yz + 9a^2$
$= (4x^2 - 12ax + 9a^2) - (y^2 + z^2 + 2yz)$
$= (2x - 3a)^2 - (y + z)^2$
$= [(2x - 3a) + (y + z)][(2x - 3a) - (y + z)]$
$= (2x - 3a + y + z)(2x - 3a - y - z).$
$= (4x^2 - 12ax + 9a^2) - (y^2 + z^2 + 2yz)$
$= (2x - 3a)^2 - (y + z)^2$
$= [(2x - 3a) + (y + z)][(2x - 3a) - (y + z)]$
$= (2x - 3a + y + z)(2x - 3a - y - z).$
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
The volume of a rectangular wall is 33 $m ^3$. If its length is 16.5 m and height 8 m, find the width of the wall.
→In the given figure, ABCD is a piece of cardboard in the shape of a trapezium in which $AB \| DC , \angle ABC =90$.
From this piece, quarter circle BEFC is removed.
Given $DC = BC =4.2 cm$ and $AE =2 cm$.
Calculate the area of the remaining piece of the cardboard.
→From this piece, quarter circle BEFC is removed.
Given $DC = BC =4.2 cm$ and $AE =2 cm$.
Calculate the area of the remaining piece of the cardboard.
Factorise : $x^2-3 x-54$
→Find three rational numbers between: $\frac{1}{2}$ and $\frac{3}{5}$
→Simplify $:\left(8 x^3 \div 125 y^3\right)^{\frac{2}{3}}$
→If $x=(4-\sqrt{15})$, find the values of $\left(x^2+\frac{1}{x^2}\right)$.
→What number decreased by $12\%$ of itself gives $1584$ ?
→Insert two irrational numbers between $3$ and $4.$
→Solve the equation:
$103 x+51 y=617 \ldots$ (i),
$97 x+49 y=583 \ldots$ (ii)
→$103 x+51 y=617 \ldots$ (i),
$97 x+49 y=583 \ldots$ (ii)
The distances of point $P (x, y)$ from the points $A (1, - 3)$ and $B (- 2, 2)$ are in the ratio $2: 3.$Show that: $5x^2+ 5y^2- 34x + 70y + 58 = 0.$
→