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BigorU [14]
3 years ago
9

Expand or factor each of the following expressions to determine which expressions are equivalent.​

Mathematics
2 answers:
Leni [432]3 years ago
7 0

Answer:

The pair of equivalent expressions are 2 and 8, 3 and 7, 4 and 5.

Step-by-step explanation:

Expand or factor each of the following expressions

1.

(4x-3y)^2=(4x)^2-(2(4x)(3y)+(3y)^2        [\because (a-b)^2=a^2-2ab+b^2]

(4x-3y)^2=16x^2-24xy+9y^2

2.

9x^2+3x-20=9x^2+15x-12x-20

9x^2+3x-20=3x(3x+5)-4(3x+5)

9x^2+3x-20=(3x+5)(3x-4)

It is same as expression 8. Therefore expression 2 and 8 are equivalent.

3.

(3x-2)(9x^2+6x+4)=(3x-2)((3x)^2+(3x(2)+2^2)

(3x-2)(9x^2+6x+4)=(3x)^3-(2)^3            [\because a^3-b^3=(a-b)(a^2+ab+b^2)]

(3x-2)(9x^2+6x+4)=27x^3-8

It is same as expression 7. Therefore expression 3 and 7 are equivalent.

4.

9x^2-24xy+16y^2=(3x)^2-2(3x)(4y)+(4y)^2

9x^2-24xy+16y^2=(3x-4y)^2        [\because (a-b)^2=a^2-2ab+b^2]

It is same as expression 5. Therefore expression 4 and 5 are equivalent.

5.

(3x-4y)^2=9x^2-24xy+16y^2

6.

(3x+2)(9x^2-6x+4)=(3x+2)((3x)^2-(3x(2)+2^2)

(3x+2)(9x^2-6x+4)=(3x)^3+(2)^3            [\because a^3+b^3=(a+b)(a^2-ab+b^2)]

(3x+2)(9x^2-6x+4)=27x^3+8

7.

27x^3-8=(3x-2)(9x^2+6x+4)

8.

(3x+5)(3x-4)=9x^2+3x-20

Therefore the pair of equivalent expressions are 2 and 8, 3 and 7, 4 and 5.

bearhunter [10]3 years ago
4 0
(3x-4y)^2=9x^2-24x+16y^2
(3x-2)(9x^2+6x+4)=27x^3-8
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