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Georgia [21]
3 years ago
15

Use the difference of two squares identity to factor each of the following expressions. (a) x²-81 (b) (3x+y)² -(2y)² (c) 4-(x-1)

² (d) (x+2)²-(y-2)²
Mathematics
1 answer:
ioda3 years ago
4 0

Answer:

a) x^2-9^2=(x+9)(x-9)

b) (3x+y)^2-(2y)^2=(3x+3y)(3x-y)

c) 2^2-(x-1)^2=(1+x)(3-x)

d) (x+2)^2-(y-2)^2=(x+y)(x-y+4)

Explanation:

Factor the expression using difference of two squares.

Formula:

a^2-b^2=(a+b)(a-b)

Part a)  x²-81

write 81 as perfect square.

x^2-9^2

a\rightarrow x

b\rightarrow 9

x^2-9^2=(x+9)(x-9)

Part b) (3x+y)² -(2y)²

a\rightarrow 3x+y

b\rightarrow 2y

(3x+y)^2-(2y)^2=(3x+y+2y)(3x+y-2y)

(3x+y)^2-(2y)^2=(3x+3y)(3x-y)

Part c) 4-(x-1)²

write 4 as perfect square,

2^2-(x-1)^2

a\rightarrow 2

b\rightarrow x-1

2^2-(x-1)^2=(2+x-1)(2-x+1)

2^2-(x-1)^2=(1+x)(3-x)

Part d) (x+2)²-(y-2)²

a\rightarrow x+2

b\rightarrow y-2

(x+2)^2-(y-2)^2=(x+2+y-2)(x+2-y+2)

(x+2)^2-(y-2)^2=(x+y)(x-y+4)

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