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Question

Use direct method to ecaluate the following products :

(i) (x + 8)(x + 3) 

(ii) (y + 5)(y - 3)

(iii) (a- 8)(a+ 2)

(iv) (b - 3)(b - 5)

(v) (3x - 2y)(2x + y)

(vi) (5a + 16)(3a -7)

(vii) (8 - b)(3 + b)


Solution

(i) (x+8)(x+3)=(x×x)+(y×3)+(5×y)+(5×3)

x2+3x+8x+24

x2+11x+24.

(ii) (y+5)(y3)=(y×y)+(y×3)+(5×y)+(5×3)

=y2+(3y)+(5y)15

=y23y+5y15

=y2+2y15

(iii) (a - 8)(a + 2) = (a×a)+(a×2)+(8)×a+(8)(2)

=a2+2a8a16

=a26a16.

(iv) (b - 3)(b - 5) = (b×b)+(b×5)+(3)×b+(3)(5)

=b25b3b+15

=b28b+15

(v) (3x - 2y)(2x+ y) = (3x×2x)+(3x×y)+(2y×2x)+(2y×y)

=6x2+3xy4xy2y2

=6x2xy2y2

(vi) (5a + 16)(3a -7) = (5a \times 3a) + (5a \times -7) + (16 \times 3a) + 16 \times - 7\)

=15a2+(35a)+48a+(112)

=15a235a+48a112

=15a2+13a112

(vii) (8 - b)(3 + b) = (8×3)+(8×b)+(b×3)+(b×b)

=24+8b3bb2

=24+5bb2


Mathematics
Concise Mathematics
Standard VIII

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