Question

level 2: match the problems to the correct simplified answers. a - 2x² + x + 15, b (2x + 5)(-x + 3); a x² + 3x - 28, b (x + 7)(x - 4); a - 12x² + 5x - 2, b (-3x + 2)(4x - 1); a x² + 8x + 12, b (x + 6)(x + 2); a x + 8, a x² + 8x + 8, a - 12x² + 11x - 2, a x² + 11x - 28, b 4 answers that do not match any questions

Explanation:

Step1: Expand \((2x + 5)(-x+3)\)

\[

$$\begin{align*} &(2x + 5)(-x + 3)\\ =&2x\times(-x)+2x\times3+5\times(-x)+5\times3\\ =&-2x^{2}+6x-5x + 15\\ =&-2x^{2}+x + 15 \end{align*}$$

\]

Step2: Expand \((x + 7)(x - 4)\)

\[

$$\begin{align*} &(x + 7)(x - 4)\\ =&x\times x+x\times(-4)+7\times x+7\times(-4)\\ =&x^{2}-4x+7x-28\\ =&x^{2}+3x - 28 \end{align*}$$

\]

Step3: Expand \((-3x + 2)(4x-1)\)

\[

$$\begin{align*} &(-3x + 2)(4x-1)\\ =&-3x\times4x-3x\times(-1)+2\times4x+2\times(-1)\\ =&-12x^{2}+3x + 8x-2\\ =&-12x^{2}+11x-2 \end{align*}$$

\]

Step4: Expand \((x + 6)(x + 2)\)

\[

$$\begin{align*} &(x + 6)(x + 2)\\ =&x\times x+x\times2+6\times x+6\times2\\ =&x^{2}+2x+6x + 12\\ =&x^{2}+8x + 12 \end{align*}$$

\]

Answer:

1. \((2x + 5)(-x + 3)\) matches \(-2x^{2}+x + 15\)
2. \((x + 7)(x - 4)\) matches \(x^{2}+3x - 28\)
3. \((-3x + 2)(4x-1)\) matches \(-12x^{2}+11x-2\)
4. \((x + 6)(x + 2)\) matches \(x^{2}+8x + 12\)
5. Un - matched answers: \(x + 8\), \(x^{2}+8x + 8\), \(x^{2}+11x-28\)