which products result in a difference of squares or a perfect square trinomial? check all that apply.\n(5x +…

which products result in a difference of squares or a perfect square trinomial? check all that apply.\n(5x + 3)(5x - 3)\n(7x + 4)(7x + 4)\n(2x + 1)(x + 2)\n(4x - 6)(x + 8)\n(x - 9)(x - 9)\n(-3x - 6)(-3x + 6)

which products result in a difference of squares or a perfect square trinomial? check all that apply.\n(5x + 3)(5x - 3)\n(7x + 4)(7x + 4)\n(2x + 1)(x + 2)\n(4x - 6)(x + 8)\n(x - 9)(x - 9)\n(-3x - 6)(-3x + 6)

Answer

Answer:

  1. (5x + 3)(5x - 3)
  2. (7x + 4)(7x + 4)
  3. (x - 9)(x - 9)
  4. (-3x - 6)(-3x + 6)

Explanation:

Step1: Recall difference - of - squares formula

The difference - of - squares formula is $(a + b)(a - b)=a^{2}-b^{2}$. For (5x + 3)(5x - 3), here $a = 5x$ and $b = 3$, so $(5x + 3)(5x - 3)=(5x)^{2}-3^{2}=25x^{2}-9$. For (-3x - 6)(-3x + 6), here $a=-3x$ and $b = 6$, so $(-3x - 6)(-3x + 6)=(-3x)^{2}-6^{2}=9x^{2}-36$.

Step2: Recall perfect - square trinomial formula

The perfect - square trinomial formulas are $(a + b)^{2}=a^{2}+2ab + b^{2}$ and $(a - b)^{2}=a^{2}-2ab + b^{2}$. For (7x + 4)(7x + 4)=(7x + 4)^{2}=(7x)^{2}+2\times7x\times4 + 4^{2}=49x^{2}+56x + 16. For (x - 9)(x - 9)=(x - 9)^{2}=x^{2}-2\times x\times9+9^{2}=x^{2}-18x + 81.

Step3: Check non - applicable products

For (2x + 1)(x + 2)=2x^{2}+4x+x + 2=2x^{2}+5x + 2, it is neither a difference of squares nor a perfect - square trinomial. For (4x - 6)(x + 8)=4x^{2}+32x-6x - 48=4x^{2}+26x - 48, it is neither a difference of squares nor a perfect - square trinomial.