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1.Multiply the binomials: (i) $$(2x + 5)$$and $$(4x – 3)$$ (ii) $$(y – 8)$$ and $$(3y – 4)$$ (iii) $$(2.5l – 0.5m)$$ and $$(2.5l + 0.5m)$$ (iv) $$(a + 3b)$$ and $$(x + 5)$$ (v) $$(2pq + 3q^2)$$ and $$(3pq – 2q^2)$$ (vi) $$(\frac { 3 }{ 4 }a^2 + 3b^2)$$ and $$4(a^2 – \frac { 2 }{ 3 } b^2)$$

(i)Multiplying the given expressions as:$$(2x + 5) \times (4x – 3)$$

$$= 2x \times (4x – 3) + 5 \times (4x – 3)$$

$$= (2x \times 4x) – (3 \times 2x) + (5 \times 4x) – (5 \times 3)$$

$$= 8x^2 – 6x + 20x – 15$$

$$= 8x^2 + 14x – 15$$

(ii)Multiplying the given expressions as: $$(y – 8) \times (3y – 4)$$

$$= y \times (3y – 4) – 8 \times (3y – 4)$$

$$= (y \times 3y) – (y \times 4) – (8 \times 3y) + (-8 \times -4)$$

$$= 3y^2 – 4y – 24y + 32$$

$$= 3y^2 – 28y + 32$$

(iii)Multiplying the given expressions as: $$(2.5l – 0.5m) × (2.5l + 0.5m)$$

$$= (2.5l \times 2.5l) + (2.5l \times 0.5m) – (0.5m \times 2.5l) – (0.5m \times 0.5m)$$

$$= 6.25l^2 + 1.25ml – 1.25ml – 0.25m^2$$

$$= 6.25l^2 + 0 – 0.25m^2$$

$$= 6.25l^2 – 0.25m^2$$

(iv)Multiplying the given expressions as: $$(a + 3b) \times (x + 5)$$

$$= a \times (x + 5) + 36 \times (x + 5)$$

$$= (a \times x) + (a \times 5) + (36 \times x) + (36 \times 5)$$

$$= ax + 5a + 3bx + 15b$$

(v) Multiplying the given expressions as:$$(2pq + 3q^2) \times (3pq – 2q^2)$$

$$= 2pq \times (3pq – 2q^2) + 3q^2 (3pq – 2q^2)$$

$$= (2pq \times 3pq) – (2pq \times 2q^2) + (3q^2 × 3pq) – (3q^2 \times 2q^2)$$

$$= 6p^2q^2 – 4pq^3 + 9pq^3 – 6q^4$$

$$= 6p^2q^2 + 5pq^3 – 6q^4$$

(vi)Multiplying the given expressions as:$$(\frac { 3 }{ 4 }a^2 + 3b^2) \times 4(a^2 – \frac { 2 }{ 3 } b^2)$$

$$=(\frac{3}4a^2+3b^2)\times(4a^2-\frac{8}3b^2)$$

$$=\frac{3}4a^2\times (4a^2-\frac{8}3b^2)+3b^2\times(4a^2-\frac{8}3b^2)$$

$$=(\frac{3}4a^2\times 4b^2) - (\frac{3}4a^2\times \frac{8}3b^2) + (3b^2\times 4a^2)-(3b^2\times\frac{8}3b^2)$$

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

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