Which products result in a difference of squares? check all that apply.

Asked by maham237 @ 30/11/2020 in Mathematics viewed by 365 People

(5z + 3)(–5z – 3)
(w – 2.5)(w + 2.5)
(8g + 1)(8g + 1)
(–4v – 9)(–4v + 9)
(6y + 7)(7y – 6)
(p – 5)(p – 5)

Answered by maham237 @ 30/11/2020

Answer:

Option 2 $(w-2.5)(w+2.5)=w^2-2.5^2\\$ and option 4 $(-4v-9)(-4v+9)=-(4v+9)(-)(4v-9)=4v^2-9^2$

Explanation:

In option 1 $(5z+3)(-5z-3)=-(5z+3)(5z+3)=-(5z+3)^2$ which is not the difference of squares

In option 2 $(w-2.5)(w+2.5)=w^2-2.5^2\\$ using the formula

$(a+b)(a-b)=a^2-b^2\\Here \\a=w,b=2.5$

Clearly, the difference of squares

In option 3 $(8g+1)(8g+1)=(8g+1)^2$ not the difference of squares

In option 4 $(-4v-9)(-4v+9)=-(4v+9)(-)(4v-9)=4v^2-9^2$

Clearly the difference of squares

In option 5 $(6y+7)(7y-6)=42y^2+13y-42$ not the difference of squares

In option 6 $(p-5)(p-5)=(p-5)^2$ not the difference of squares

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