Expanding Brackets (OCR GCSE Maths: Higher): Exam Questions

Expand and simplify       $3\left(m+4\right)-2(4m+1)$

Expand and simplify         $5\left(p+3\right)-2\left(1-2p\right)$

Expand and simplify     $\left(p+9\right)\left(p-4\right)$

Expand and simplify        $(x+4)(x+6)$

Expand and simplify  $\left(m+3\right)\left(m+10\right)$

Expand and simplify.

$(x-7)(x+3)$

Factorise.

$x^2-49$

Expand and simplify         $\left(x-5\right)\left(x+3\right)$

Expand and simplify            $\left(y-2\right)\left(y-5\right)$

Expand and simplify           $\left(y+2\right)\left(y+5\right)$

Expand and simplify        $\left(m+7\right)\left(m+3\right)$

Expand and simplify

                        $\left(2x+1\right)\left(x-4\right)$

Expand and simplify      $\left(2x+3\right)\left(x-8\right)$

Expand and simplify                $\left(2t-3\right)\left(t+5\right)$

Expand and simplify               ${\left(w-5\right)}^2$

Expand and simplify  $\left(y+4\right)\left(2-y\right)$

Expand and simplify  $3x(2x+3)–x(3x+5)$

Expand and simplify fully  $4(2c+3)–(5c–1)$

Show that $(x+1)(x+2)(x+3)$ can be written in the form $a{x}^3+b{x}^2+cx+d$ where  $a,b,c$ and $d$ are positive integers.

Show that

$\left(3x-1\right)\left(x+5\right)\left(4x-3\right)=12x^3+47x^2-62x+15$

for all values of $x$.

Simplify fully $\left(\sqrt{a}+\sqrt{4b}\right)\left(\sqrt{a}-2\sqrt{b}\right)$

Show that $(2x+1)(x+3)(3x+7)$ can be written in the form $a{x}^3+b{x}^2+cx+d$   where $a,b,c$ and $d$ are integers.

Solve           ${\left(1-x\right)}^2<\frac{9}{25}$

The area of square $ABCD$ is $10$ cm². Show that $x^2+6x=1$

Expand and simplify.

$\left(x+1\right)\left(x-1\right)\left(x+2\right)$

$\left(x+a\right)\left(x+3\right)\left(2x+1\right)=b{x}^3+c{x}^2+dx-12$

Find the value of $a,$ $b$, $c$ and $d$.

$a$ = ..................

$b$ = ..................

$c$ = ..................

$d$ = ..................

Expand and simplify.

$(2x-1)(x+5)(3x-2)$

$\left(x+3\right)\left(x-4\right)\left(x+5\right)$ is identical to $x^3+a{x}^2-17x+b$

Find the value of $a$ and the value of $b$.

$$\begin{gathered} a=..................................................... \\ b=..................................................... \end{gathered}$$

Expand and simplify

            $5x\left(x+2\right)\left(3x-4\right)$

Given that $\left(8-\sqrt{x}\right)\left(5+\sqrt{x}\right)=y\sqrt{x}+21$  where $x$ is a prime number and $y$ is an integer, find the value of $x$ and the value of $y$. Show each stage of your working clearly.

x = .......................................................
y = ...................................................... 

Solve $(2x+5{)}^2=(2x+3\left)\right(2x–1)$

$x=$ ...................................... 

The functions $\mathrm{f}$and $\mathrm{g}$ are defined as

$\begin{array}{rcl}\mathrm{f}\left(x\right)& =& x^2+6\\ \mathrm{g}\left(x\right)& =& x–10\end{array}$

Solve the equation $\mathrm{fg}\left(x\right)=\mathrm{f}\left(x\right)$

Show clear algebraic working.

Expand and simplify $(4x+1)(x–3)(5x+6)$

Show that $x(x-1)\left(x+1\right)=x^3-x$

Expand and simplify fully $\left(x-3\right)\left(x+2\right)\left(x+5\right)$

$s$ and$t$are positive integers.

$(x+s)(x–t)$ is expanded and simplified.
The answer is $x^2+kx–40$ where k is a positive integer.

Work out the smallest possible value of $k$.

Expand and simplify $(3x^2+2)(2x+5)–6x(x^2–3)$

Expand and simplify   $(x-4){(2x+3y)}^2$

$(2x+3)(x+a)(bx-1)\equiv 4x^3-4x^2-11x+6$

Find the values of $a$ and $b$.