Algebraic Expressions

Exercise 9.4

Question 1: Multiply the binomials.

(i) `(2x + 5)` and `(4x – 3)`

Answer: `(2x + 5)(4x - 3)`
`= 2x × 4x - 2x × 3 + 5 × 4x - 5 × 3`
`= 8x^2 - 6x + 20x -15`
`= 8x^2 + 14x -15`

(ii) `(y – 8)` and `(3y – 4)`

Answer: `( y - 8)(3y - 4)`
`= y × 3y - 4y - 8 × 3y + 32`
`= 3y^2 - 4y - 24y + 32`
`= 3y^2 - 28y + 32`


(iii) `(2.5l – 0.5m) and (2.5l + 0.5m)`

Answer: `(2.5l - 0.5m)(2.5l + 0.5)`
Using `(a+b)(a-b) = a^2 - b^2`
We get `= 6.25 l^2 - 0.25 m^2`

(iv) `(a + 3b)` and `(x + 5)`

Answer: `= ax + 5a + 3bx + 15b`

(v)`(2pq + 3q^2)` and `(3pq – 2q^2)`

Answer: `= 2pq × 3pq - 2pq × 2q^2 + 3q^2 × 3pq - 3q^2 × 2q^2`
`= 6p^2q^2 - 4pq^3 + 9pq^3 - 6q^4`
`= 6p^2q^2 - 5pq^3 - 6p^4`

(vi) `(3/4a^2+3b^2)xx4(a^2-2/3b^2)`

Answer: `=3/4a^2\xx4a^2-3/4a^2\xx8/3b^2+12a^2b^2-8b^2`

`=3a^4-2a^2b^2+12a^2b^2-8b^4`

`=3a^4-8b^2+10a^2b^2`


Question 2: Find the product.

(i) `(5 – 2x) (3 + x)`

Answer: `= 15 + 5x - 6x - 2x^2`
`= 15 - x - x^2`

(ii) `(x + 7y) (7x – y)`

Answer: `= 7x^2 - xy + 49xy - 7y^2`
`= 7x^2 - 7y^2 + 48xy`

iii) `(a^2+ b) (a + b^2)`

Answer: `a^2 xx\ a + a^2\xx\b + a\ xx\ b + b^3`
`= a^3 + a^2b + ab + b^3`
`= a^3 + b^3 + a^2b + ab`

(iv) `(p^2– q^2) (2p + q)`

Answer: `= 2p^3 + p^2q - 2pq^2 - q^3`
`= 2p^3 - q^3 + p^2q - 2pq^2`

Question 3: Simplify.

(i) `(x^2– 5) (x + 5) + 25`

Answer: `= x^3 + 5x^2 - 5x - 25 + 25`
`= x^3 + 5x^2 -5x`

(ii) `(a^2+ 5) (b^3+ 3) + 5`

Answer: `a^2b^3 + 3a^2 + 5b^3 + 15 + 5`
`= a^2b^3 + 5b^3 + 3a^2 + 20`

(iv) `(a + b) (c – d) ``+ (a – b) (c + d) + 2 (ac + bd)`

Answer: `= (ac - ad + bc - bd) + (ac + ad - bc - bd)`` + (2ac + 2bd)`
`= ac - ad + bc - bd + ac + ad - bc ``- bd + 2ac + 2bd= 4ac`

(v) `(x + y)(2x + y) + (x + 2y)(x – y)`

Answer: `=2x^2 + xy + 2xy + y^2 + x^2 - xy + 2xy - 2y^2`
`= 3x^2 + 4xy - y^2`

(vi) `(x + y)(x^2– xy + y^2)`

Answer: `= x^3 - x^2y + xy^2 + x^2y - xy^2 + y^3`
`= x^3 + y^3`

(vii) `(1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y`

Answer: `= 2.25x^2 + 6xy + 4.5x - 6xy - 16y^2`` - 12y - 4.5x + 12y`
`= 2.25x^2 - 16y^2`

(viii) `(a + b + c)(a + b – c)`

Answer: `= a^2 + ab - ac + ab + b^2 - bc + ac + bc - c^2`
`= a^2 + b^2 - c^2 + 2ab`



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