Factorise: 2(x + y)^2 - 9(x + y) - 5 - Vidyadip

Question

Factorise: $2(x + y)^2 - 9(x + y) - 5$

✓

Answer

Let $x + y = z$
Then, $2(x + y)^2 - 9(x + y) - 5$
$= 2z^2 - 9z - 5$
$= 2z^2 - 10z + z - 5$
$= 2z(z - 5) + 1(z - 5)$
$= (z - 5)(2z + 1)$
Now, replacing $z$ by $(x + y)$, we get $2(x + y)^2 - 9(x + y) - 5$
$= [(x + y) - 5][(2(x + y) + 1)] = (x + y - 5)(2x + 2y + 1)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Factorisation of Polynomials→Factorisation of Polynomials — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

Prove that: $\frac{\text{abc}}{\text{a}^{-1}\text{b}^{-1}+\text{b}^{-1}\text{c}^{-1}+\text{c}^{-1}\text{a}^{-1}}=\text{abc}$

If both $x -2$ and $x -\frac{1}{2}$ are factors of $px ^2+5 x + r$, show that $p = r$.

The polynomials $\left(2 x^3+x^2-a x+2\right)$ and $\left(2 x^3-3 x^2-3 x+a\right)$ when divided by $(x-2)$ leave the same remainder. Find the value of $a$.

If $O$ is a point within a quadrilateral $ABCD,$ show that $OA + OB + OC + OD > AC + BD.$

Factorize the following expressions:
$1029-3 x^3$

If $x^2+\frac{1}{x^2}=34$, find $x^3+\frac{1}{x^3}-9$.

Evaluate:
$\frac{(25)^{\frac{5}{2}}\times(729)^{\frac{1}{3}}}{(125)^{\frac{2}{3}}\times(27)^{\frac{2}{3}}\times8^{\frac{4}{3}}}$

The radius of a cone is $7\ cm$ and area of curved surface is $176cm^2.$ Find the slant height.

Multiply: $(9x^2 + 25y^2 + 15xy + 12x - 20y + 16) by (3x - 5y + 4)$

The angles of a triangles are in the ratio $2 : 3 : 4$ Find the angles.