Question

Find the product

i) (2x+3y)(2x-3y)
ii) (x+2y)(x+2y)
iii) (x+2)(x+5)

iv) (3x-4y)(3x-4y)​

Answer 1

Answer:

1.(2x+3y)(2x-3y)

=4x²-9y²

2.(x+2y)(x+2y)

=x²+4xy+4y²

3.(x+2)(x+5)

=x²+7x+10

4.(3x-4y)(3x-4y)

=9x-24xy+16y²

Explanation:

1.(2x)²-(3y)²

=4x²-9y²

2. x(x+2y)+2y(x+2y)

=x²+2xy+2xy+4y²

=x²+4xy+4y²

3.x(x+5)+2(x+5)

=x²+5x+2x+10

=x²+7x+10

4.3(3x-4y)-4y(3x-4y)

=9x²-12xy-12xy+16y²

=9x-24xy+16y²

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Answer 2

i) Given Equation is (2x + 3y)(2x - 3y)

- It is in the form of (a+b) (a-b) = a²-b²

= > 4x²- 6xy + 6xy - 9y²

= > 4x² - 9y²

ii) Given Equation is (x+2y)(x+2y)

- It is in form of (a+b)² = a² + b² +2ab

a=x & b=2y

(x+2y)²= (x)² + (2y²)+2(x)(2y)

(x+2y)²= x²+ 4y²+ 4xy

iii) Given Equation is ( x + 5 )( x + 2 )

- It is in the form of (x+a) (x+b) = x² + (a+b)x +ab

Now ⤵️

= x² + ( 5 + 2 )x + 5 × 2

= x² + 7x + 10

iv) (3x - 4y)(3x - 4y) = (3x - 4y)²

- It is in the form of (a - b)²= a² + b² -2ab

a = 3x & b= 4y

(3x - 4y)²= (3x)² + (4y)²- 2(3x)(4y)

(3x - 4y)²= 9x+ 16y- 24xy